diff --git a/pandas-stubs/_libs/tslibs/period.pyi b/pandas-stubs/_libs/tslibs/period.pyi
index 897153c2e..55b1a2bfb 100644
--- a/pandas-stubs/_libs/tslibs/period.pyi
+++ b/pandas-stubs/_libs/tslibs/period.pyi
@@ -12,7 +12,10 @@ from pandas import (
     Timedelta,
     TimedeltaIndex,
 )
-from typing_extensions import TypeAlias
+from typing_extensions import (
+    Self,
+    TypeAlias,
+)
 
 from pandas._libs.tslibs import NaTType
 from pandas._libs.tslibs.offsets import BaseOffset
@@ -87,15 +90,23 @@ class Period(PeriodMixin):
     @overload
     def __sub__(self, other: TimedeltaIndex) -> PeriodIndex: ...
     @overload
-    def __add__(self, other: _PeriodAddSub) -> Period: ...
+    def __add__(self, other: _PeriodAddSub) -> Self: ...
     @overload
     def __add__(self, other: NaTType) -> NaTType: ...
     @overload
     def __add__(self, other: Index) -> PeriodIndex: ...
+    # Ignored due to indecipherable error from mypy:
+    # Forward operator "__add__" is not callable  [misc]
     @overload
-    def __add__(
-        self, other: Series[BaseOffset] | Series[Timedelta]
-    ) -> Series[Period]: ...  # pyrefly: ignore[bad-specialization]
+    def __radd__(self, other: _PeriodAddSub) -> Self: ...  # type: ignore[misc]
+    @overload
+    def __radd__(self, other: NaTType) -> NaTType: ...
+    # Real signature is -> PeriodIndex, but conflicts with Index.__add__
+    # Changing Index is very hard due to Index inheritance
+    #   Signatures of "__radd__" of "Period" and "__add__" of "Index"
+    #   are unsafely overlapping
+    @overload
+    def __radd__(self, other: Index) -> PeriodIndex: ...
     #  ignore[misc] here because we know all other comparisons
     #  are False, so we use Literal[False]
     @overload
@@ -168,18 +179,6 @@ class Period(PeriodMixin):
     def __ne__(self, other: np_ndarray[ShapeT, np.object_]) -> np_ndarray[ShapeT, np.bool]: ...  # type: ignore[overload-overlap]
     @overload
     def __ne__(self, other: object) -> Literal[True]: ...
-    # Ignored due to indecipherable error from mypy:
-    # Forward operator "__add__" is not callable  [misc]
-    @overload
-    def __radd__(self, other: _PeriodAddSub) -> Period: ...  # type: ignore[misc]
-    # Real signature is -> PeriodIndex, but conflicts with Index.__add__
-    # Changing Index is very hard due to Index inheritance
-    #   Signatures of "__radd__" of "Period" and "__add__" of "Index"
-    #   are unsafely overlapping
-    @overload
-    def __radd__(self, other: Index) -> Index: ...
-    @overload
-    def __radd__(self, other: NaTType) -> NaTType: ...
     @property
     def day(self) -> int: ...
     @property
diff --git a/pandas-stubs/_libs/tslibs/timedeltas.pyi b/pandas-stubs/_libs/tslibs/timedeltas.pyi
index 9ad5e0e68..a8adc91f3 100644
--- a/pandas-stubs/_libs/tslibs/timedeltas.pyi
+++ b/pandas-stubs/_libs/tslibs/timedeltas.pyi
@@ -1,6 +1,9 @@
 # pyright: strict
-import datetime as dt
-from datetime import timedelta
+from datetime import (
+    date,
+    datetime,
+    timedelta,
+)
 from typing import (
     ClassVar,
     Literal,
@@ -135,9 +138,9 @@ class Timedelta(timedelta):
     def ceil(self, freq: str | BaseOffset) -> Self: ...
     @property
     def resolution_string(self) -> str: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
-    def __add__(self, other: dt.datetime | np.datetime64) -> Timestamp: ...
+    def __add__(self, other: datetime | np.datetime64) -> Timestamp: ...
     @overload
     def __add__(self, other: timedelta | np.timedelta64) -> Self: ...
     @overload
@@ -145,7 +148,7 @@ class Timedelta(timedelta):
     @overload
     def __add__(self, other: Period) -> Period: ...
     @overload
-    def __add__(self, other: dt.date) -> dt.date: ...
+    def __add__(self, other: date) -> date: ...
     @overload
     def __add__(
         self, other: np_ndarray[ShapeT, np.timedelta64]
@@ -155,13 +158,13 @@ class Timedelta(timedelta):
         self, other: np_ndarray[ShapeT, np.datetime64]
     ) -> np_ndarray[ShapeT, np.datetime64]: ...
     @overload
-    def __radd__(self, other: dt.datetime | np.datetime64) -> Timestamp: ...  # type: ignore[misc]
+    def __radd__(self, other: datetime | np.datetime64) -> Timestamp: ...  # type: ignore[misc]
     @overload
     def __radd__(self, other: timedelta | np.timedelta64) -> Self: ...
     @overload
     def __radd__(self, other: NaTType) -> NaTType: ...
     @overload
-    def __radd__(self, other: dt.date) -> dt.date: ...
+    def __radd__(self, other: date) -> date: ...
     @overload
     def __radd__(
         self, other: np_ndarray[ShapeT, np.timedelta64]
@@ -170,9 +173,9 @@ class Timedelta(timedelta):
     def __radd__(
         self, other: np_ndarray[ShapeT, np.datetime64]
     ) -> np_ndarray[ShapeT, np.datetime64]: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
-    def __sub__(self, other: timedelta | Timedelta | np.timedelta64) -> Timedelta: ...
+    def __sub__(self, other: timedelta | Timedelta | np.timedelta64) -> Self: ...
     @overload
     def __sub__(self, other: NaTType) -> NaTType: ...
     @overload
@@ -182,11 +185,9 @@ class Timedelta(timedelta):
     @overload
     def __sub__(self, other: pd.TimedeltaIndex) -> TimedeltaIndex: ...
     @overload
-    def __sub__(self, other: Series[pd.Timedelta]) -> Series[pd.Timedelta]: ...
-    @overload
-    def __rsub__(self, other: timedelta | Timedelta | np.timedelta64) -> Timedelta: ...
+    def __rsub__(self, other: timedelta | Timedelta | np.timedelta64) -> Self: ...
     @overload
-    def __rsub__(self, other: dt.datetime | Timestamp | np.datetime64) -> Timestamp: ...  # type: ignore[misc]
+    def __rsub__(self, other: datetime | Timestamp | np.datetime64) -> Timestamp: ...  # type: ignore[misc]
     @overload
     def __rsub__(self, other: NaTType) -> NaTType: ...
     @overload
@@ -205,44 +206,31 @@ class Timedelta(timedelta):
     ) -> np_ndarray[ShapeT, np.timedelta64]: ...
     @overload
     def __rsub__(self, other: pd.TimedeltaIndex) -> pd.TimedeltaIndex: ...
-    def __neg__(self) -> Timedelta: ...
-    def __pos__(self) -> Timedelta: ...
-    def __abs__(self) -> Timedelta: ...
-    # Override due to more types supported than dt.timedelta
+    def __neg__(self) -> Self: ...
+    def __pos__(self) -> Self: ...
+    def __abs__(self) -> Self: ...
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
-    def __mul__(self, other: float) -> Timedelta: ...
+    def __mul__(self, other: float) -> Self: ...
     @overload
     def __mul__(
-        self, other: np_ndarray[ShapeT, np.integer] | np_ndarray[ShapeT, np.floating]
+        self, other: np_ndarray[ShapeT, np.bool_ | np.integer | np.floating]
     ) -> np_ndarray[ShapeT, np.timedelta64]: ...
     @overload
-    def __mul__(self, other: Series[int]) -> Series[Timedelta]: ...
-    @overload
-    def __mul__(self, other: Series[float]) -> Series[Timedelta]: ...
-    @overload
-    def __mul__(self, other: Index[int] | Index[float]) -> TimedeltaIndex: ...
-    @overload
-    def __rmul__(self, other: float) -> Timedelta: ...
+    def __rmul__(self, other: float) -> Self: ...
     @overload
     def __rmul__(
-        self, other: np_ndarray[ShapeT, np.floating] | np_ndarray[ShapeT, np.integer]
+        self, other: np_ndarray[ShapeT, np.bool_ | np.integer | np.floating]
     ) -> np_ndarray[ShapeT, np.timedelta64]: ...
-    @overload
-    def __rmul__(self, other: Series[int]) -> Series[Timedelta]: ...
-    @overload
-    def __rmul__(self, other: Series[float]) -> Series[Timedelta]: ...
-    # maybe related to https://github.com/python/mypy/issues/10755
-    @overload
-    def __rmul__(self, other: Index[int] | Index[float]) -> TimedeltaIndex: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     # error: Signature of "__floordiv__" incompatible with supertype "timedelta"
     @overload  # type: ignore[override]
     def __floordiv__(self, other: timedelta | Timedelta | np.timedelta64) -> int: ...
     @overload
-    def __floordiv__(self, other: float) -> Timedelta: ...
+    def __floordiv__(self, other: float) -> Self: ...
     @overload
     def __floordiv__(
-        self, other: np_ndarray[ShapeT, np.integer] | np_ndarray[ShapeT, np.floating]
+        self, other: np_ndarray[ShapeT, np.integer | np.floating]
     ) -> np_ndarray[ShapeT, np.timedelta64]: ...
     @overload
     def __floordiv__(
@@ -266,14 +254,14 @@ class Timedelta(timedelta):
     def __rfloordiv__(
         self, other: np_ndarray[ShapeT, np.timedelta64]
     ) -> np_ndarray[ShapeT, np.int_]: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
     def __truediv__(self, other: timedelta | Timedelta | NaTType) -> float: ...
     @overload
-    def __truediv__(self, other: float) -> Timedelta: ...
+    def __truediv__(self, other: float) -> Self: ...
     @overload
     def __truediv__(
-        self, other: np_ndarray[ShapeT, np.integer] | np_ndarray[ShapeT, np.floating]
+        self, other: np_ndarray[ShapeT, np.integer | np.floating]
     ) -> np_ndarray[ShapeT, np.timedelta64]: ...
     @overload
     def __truediv__(self, other: Series[Timedelta]) -> Series[float]: ...
@@ -284,7 +272,7 @@ class Timedelta(timedelta):
     @overload
     def __truediv__(self, other: Index[int] | Index[float]) -> TimedeltaIndex: ...
     def __rtruediv__(self, other: timedelta | Timedelta | NaTType) -> float: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload
     def __eq__(self, other: timedelta | Timedelta | np.timedelta64) -> bool: ...  # type: ignore[overload-overlap] # pyright: ignore[reportOverlappingOverload]
     @overload
@@ -297,7 +285,7 @@ class Timedelta(timedelta):
     ) -> np_ndarray[ShapeT, np.bool_]: ...
     @overload
     def __eq__(self, other: object) -> Literal[False]: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload
     def __ne__(self, other: timedelta | Timedelta | np.timedelta64) -> bool: ...  # type: ignore[overload-overlap] # pyright: ignore[reportOverlappingOverload]
     @overload
@@ -310,18 +298,18 @@ class Timedelta(timedelta):
     ) -> np_ndarray[ShapeT, np.bool_]: ...
     @overload
     def __ne__(self, other: object) -> Literal[True]: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
-    def __mod__(self, other: timedelta) -> Timedelta: ...
+    def __mod__(self, other: timedelta) -> Self: ...
     @overload
-    def __mod__(self, other: float) -> Timedelta: ...
+    def __mod__(self, other: float) -> Self: ...
     @overload
     def __mod__(self, other: Series[int] | Series[float]) -> Series[Timedelta]: ...
     @overload
     def __mod__(self, other: Index[int] | Index[float]) -> TimedeltaIndex: ...
     @overload
     def __mod__(
-        self, other: np_ndarray[ShapeT, np.integer] | np_ndarray[ShapeT, np.floating]
+        self, other: np_ndarray[ShapeT, np.integer | np.floating]
     ) -> np_ndarray[ShapeT, np.timedelta64]: ...
     @overload
     def __mod__(
@@ -330,7 +318,7 @@ class Timedelta(timedelta):
     def __divmod__(self, other: timedelta) -> tuple[int, Timedelta]: ...
     # Mypy complains Forward operator "<inequality op>" is not callable, so ignore misc
     # for le, lt ge and gt
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
     def __le__(self, other: timedelta | Timedelta | np.timedelta64) -> bool: ...  # type: ignore[misc]
     @overload
@@ -341,7 +329,7 @@ class Timedelta(timedelta):
     ) -> np_ndarray[ShapeT, np.bool_]: ...
     @overload
     def __le__(self, other: Series[pd.Timedelta]) -> Series[bool]: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
     def __lt__(self, other: timedelta | Timedelta | np.timedelta64) -> bool: ...  # type: ignore[misc]
     @overload
@@ -352,7 +340,7 @@ class Timedelta(timedelta):
     ) -> np_ndarray[ShapeT, np.bool_]: ...
     @overload
     def __lt__(self, other: Series[pd.Timedelta]) -> Series[bool]: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
     def __ge__(self, other: timedelta | Timedelta | np.timedelta64) -> bool: ...  # type: ignore[misc]
     @overload
@@ -363,7 +351,7 @@ class Timedelta(timedelta):
     ) -> np_ndarray[ShapeT, np.bool_]: ...
     @overload
     def __ge__(self, other: Series[pd.Timedelta]) -> Series[bool]: ...
-    # Override due to more types supported than dt.timedelta
+    # Override due to more types supported than timedelta
     @overload  # type: ignore[override]
     def __gt__(self, other: timedelta | Timedelta | np.timedelta64) -> bool: ...  # type: ignore[misc]
     @overload
diff --git a/pandas-stubs/_typing.pyi b/pandas-stubs/_typing.pyi
index b852fcc65..9e24a97a5 100644
--- a/pandas-stubs/_typing.pyi
+++ b/pandas-stubs/_typing.pyi
@@ -173,7 +173,8 @@ RandomState: TypeAlias = (
 )
 
 # dtypes
-NpDtype: TypeAlias = str | np.dtype[np.generic] | type[str | complex | bool | object]
+NpDtypeNoStr: TypeAlias = np.dtype[np.generic] | type[complex | bool | object]
+NpDtype: TypeAlias = str | NpDtypeNoStr | type[str]
 Dtype: TypeAlias = ExtensionDtype | NpDtype
 
 # AstypeArg is more carefully defined here as compared to pandas
@@ -847,19 +848,21 @@ MaskType: TypeAlias = Series[bool] | np_ndarray_bool | list[bool]
 
 T_INT = TypeVar("T_INT", bound=int)
 T_COMPLEX = TypeVar("T_COMPLEX", bound=complex)
-SeriesDTypeNoDateTime: TypeAlias = (
-    str
-    | bytes
+SeriesDTypeNoStrDateTime: TypeAlias = (
+    bytes
     | bool
     | int
     | float
     | complex
-    | Dtype
+    | NpDtypeNoStr
+    | ExtensionDtype
     | Period
     | Interval
     | CategoricalDtype
     | BaseOffset
-    | list[str]
+)
+SeriesDTypeNoDateTime: TypeAlias = (
+    str | SeriesDTypeNoStrDateTime | type[str] | list[str]
 )
 SeriesDType: TypeAlias = (
     SeriesDTypeNoDateTime
@@ -869,6 +872,9 @@ SeriesDType: TypeAlias = (
     | datetime.timedelta  # includes pd.Timedelta
 )
 S1 = TypeVar("S1", bound=SeriesDType, default=Any)
+S1_CO_NSDT = TypeVar(
+    "S1_CO_NSDT", bound=SeriesDTypeNoStrDateTime, default=Any, covariant=True
+)
 S1_CT_NDT = TypeVar(
     "S1_CT_NDT", bound=SeriesDTypeNoDateTime, default=Any, contravariant=True
 )
diff --git a/pandas-stubs/core/indexes/base.pyi b/pandas-stubs/core/indexes/base.pyi
index 32f2f6297..112cb7dff 100644
--- a/pandas-stubs/core/indexes/base.pyi
+++ b/pandas-stubs/core/indexes/base.pyi
@@ -21,7 +21,9 @@ from typing import (
 
 from _typeshed import (
     SupportsAdd,
+    SupportsMul,
     SupportsRAdd,
+    SupportsRMul,
 )
 import numpy as np
 from pandas import (
@@ -48,12 +50,15 @@ from typing_extensions import (
 )
 
 from pandas._libs.interval import _OrderableT
+from pandas._libs.tslibs.timedeltas import Timedelta
 from pandas._typing import (
     C2,
     S1,
     S1_CO,
+    S1_CO_NSDT,
     S1_CT,
     T_COMPLEX,
+    T_INT,
     AnyAll,
     ArrayLike,
     AxesData,
@@ -82,8 +87,10 @@ from pandas._typing import (
     np_ndarray_anyint,
     np_ndarray_bool,
     np_ndarray_complex,
+    np_ndarray_dt,
     np_ndarray_float,
     np_ndarray_str,
+    np_ndarray_td,
     type_t,
 )
 
@@ -728,16 +735,115 @@ class Index(IndexOpsMixin[S1]):
         ),
     ) -> Index[complex]: ...
     @overload
+    def __mul__(self: Index[Never], other: complex | _ListLike | Index) -> Index: ...
+    @overload
+    def __mul__(self, other: Index[Never]) -> Index: ...
+    @overload
+    def __mul__(self, other: np_ndarray_dt) -> Never: ...
+    # pandas-dev/pandas#62524
+    @overload
+    def __mul__(  # type: ignore[overload-overlap]
+        self: Index[bool] | Index[int] | Index[float], other: Sequence[timedelta]
+    ) -> Index[Timedelta]: ...
+    @overload
     def __mul__(
-        self: Index[int] | Index[float], other: timedelta
+        self: Index[bool] | Index[int] | Index[float],
+        other: timedelta | Sequence[Timedelta] | np.timedelta64 | np_ndarray_td,
     ) -> TimedeltaIndex: ...
     @overload
+    def __mul__(self: Index[T_INT], other: bool | Sequence[bool]) -> Index[T_INT]: ...
+    @overload
+    def __mul__(self: Index[float], other: int | Sequence[int]) -> Index[float]: ...
+    @overload
     def __mul__(
-        self, other: float | Sequence[float] | Index[int] | Index[float]
-    ) -> Self: ...
+        self: Index[complex], other: float | Sequence[float]
+    ) -> Index[complex]: ...
+    @overload
+    def __mul__(
+        self: Index[S1_CT],
+        other: (
+            SupportsRMul[S1_CT, S1_CO_NSDT] | Sequence[SupportsRMul[S1_CT, S1_CO_NSDT]]
+        ),
+    ) -> Index[S1_CO_NSDT]: ...
+    @overload
+    def __mul__(
+        self: Index[T_COMPLEX], other: np_ndarray_bool | Index[bool]
+    ) -> Index[T_COMPLEX]: ...
+    @overload
+    def __mul__(
+        self: Index[bool], other: np_ndarray_anyint | Index[int]
+    ) -> Index[int]: ...
+    @overload
+    def __mul__(
+        self: Index[T_COMPLEX], other: np_ndarray_anyint | Index[int]
+    ) -> Index[T_COMPLEX]: ...
+    @overload
+    def __mul__(
+        self: Index[bool] | Index[int], other: np_ndarray_float | Index[float]
+    ) -> Index[float]: ...
+    @overload
+    def __mul__(
+        self: Index[T_COMPLEX], other: np_ndarray_float | Index[float]
+    ) -> Index[T_COMPLEX]: ...
+    @overload
+    def __mul__(
+        self: Index[T_COMPLEX], other: np_ndarray_complex | Index[complex]
+    ) -> Index[complex]: ...
+    @overload
+    def __rmul__(self: Index[Never], other: complex | _ListLike | Index) -> Index: ...
+    @overload
+    def __rmul__(self, other: Index[Never]) -> Index: ...
+    @overload
+    def __rmul__(self, other: np_ndarray_dt) -> Never: ...
+    # pandas-dev/pandas#62524
+    @overload
+    def __rmul__(  # type: ignore[overload-overlap]
+        self: Index[bool] | Index[int] | Index[float], other: Sequence[timedelta]
+    ) -> Index[Timedelta]: ...
+    @overload
     def __rmul__(
-        self, other: float | Sequence[float] | Index[int] | Index[float]
-    ) -> Self: ...
+        self: Index[bool] | Index[int] | Index[float],
+        other: timedelta | Sequence[Timedelta] | np.timedelta64 | np_ndarray_td,
+    ) -> TimedeltaIndex: ...
+    @overload
+    def __rmul__(self: Index[T_INT], other: bool | Sequence[bool]) -> Index[T_INT]: ...
+    @overload
+    def __rmul__(self: Index[float], other: int | Sequence[int]) -> Index[float]: ...
+    @overload
+    def __rmul__(
+        self: Index[complex], other: float | Sequence[float]
+    ) -> Index[complex]: ...
+    @overload
+    def __rmul__(
+        self: Index[S1_CT],
+        other: (
+            SupportsMul[S1_CT, S1_CO_NSDT] | Sequence[SupportsMul[S1_CT, S1_CO_NSDT]]
+        ),
+    ) -> Index[S1_CO_NSDT]: ...
+    @overload
+    def __rmul__(
+        self: Index[T_COMPLEX], other: np_ndarray_bool | Index[bool]
+    ) -> Index[T_COMPLEX]: ...
+    @overload
+    def __rmul__(
+        self: Index[bool], other: np_ndarray_anyint | Index[int]
+    ) -> Index[int]: ...
+    @overload
+    def __rmul__(
+        self: Index[T_COMPLEX], other: np_ndarray_anyint | Index[int]
+    ) -> Index[T_COMPLEX]: ...
+    @overload
+    def __rmul__(
+        self: Index[bool] | Index[int], other: np_ndarray_float | Index[float]
+    ) -> Index[float]: ...
+    @overload
+    def __rmul__(
+        self: Index[T_COMPLEX], other: np_ndarray_float | Index[float]
+    ) -> Index[T_COMPLEX]: ...
+    @overload
+    def __rmul__(
+        self: Index[T_COMPLEX], other: np_ndarray_complex | Index[complex]
+    ) -> Index[complex]: ...
     def __floordiv__(
         self, other: float | Sequence[float] | Index[int] | Index[float]
     ) -> Self: ...
diff --git a/pandas-stubs/core/indexes/datetimelike.pyi b/pandas-stubs/core/indexes/datetimelike.pyi
index bf5556595..0c0087e6b 100644
--- a/pandas-stubs/core/indexes/datetimelike.pyi
+++ b/pandas-stubs/core/indexes/datetimelike.pyi
@@ -1,7 +1,9 @@
 import numpy as np
 from pandas.core.indexes.extension import ExtensionIndex
-from pandas.core.indexes.timedeltas import TimedeltaIndex
-from typing_extensions import Self
+from typing_extensions import (
+    Never,
+    Self,
+)
 
 from pandas._libs.tslibs import BaseOffset
 from pandas._typing import (
@@ -9,6 +11,7 @@ from pandas._typing import (
     AxisIndex,
     GenericT_co,
     TimeUnit,
+    np_ndarray_complex,
 )
 
 class DatetimeIndexOpsMixin(ExtensionIndex[S1, GenericT_co]):
@@ -30,9 +33,12 @@ class DatetimeIndexOpsMixin(ExtensionIndex[S1, GenericT_co]):
     def argmax(
         self, axis: AxisIndex | None = None, skipna: bool = True, *args, **kwargs
     ) -> np.int64: ...
-    def __rsub__(  # type: ignore[misc,override] # pyright: ignore[reportIncompatibleMethodOverride]
-        self, other: DatetimeIndexOpsMixin
-    ) -> TimedeltaIndex: ...
+    def __mul__(  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
+        self, other: np_ndarray_complex
+    ) -> Never: ...
+    def __rmul__(  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
+        self, other: np_ndarray_complex
+    ) -> Never: ...
 
 class DatetimeTimedeltaMixin(DatetimeIndexOpsMixin[S1, GenericT_co]):
     @property
diff --git a/pandas-stubs/core/indexes/datetimes.pyi b/pandas-stubs/core/indexes/datetimes.pyi
index 12af992f7..16e1a8c22 100644
--- a/pandas-stubs/core/indexes/datetimes.pyi
+++ b/pandas-stubs/core/indexes/datetimes.pyi
@@ -62,20 +62,19 @@ class DatetimeIndex(
     # various ignores needed for mypy, as we do want to restrict what can be used in
     # arithmetic for these types
     def __add__(  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
-        self, other: timedelta | TimedeltaIndex | BaseOffset
-    ) -> DatetimeIndex: ...
-    def __radd__(  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
-        self, other: timedelta | TimedeltaIndex | BaseOffset
-    ) -> DatetimeIndex: ...
+        self, other: timedelta | BaseOffset
+    ) -> Self: ...
+    def __radd__(  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
+        self, other: timedelta | BaseOffset
+    ) -> Self: ...
     @overload  # type: ignore[override]
     def __sub__(
-        self,
-        other: timedelta | np.timedelta64 | np_ndarray_td | TimedeltaIndex | BaseOffset,
-    ) -> DatetimeIndex: ...
+        self, other: datetime | np.datetime64 | np_ndarray_dt | Self
+    ) -> TimedeltaIndex: ...
     @overload
     def __sub__(  # pyright: ignore[reportIncompatibleMethodOverride]
-        self, other: datetime | np.datetime64 | np_ndarray_dt | DatetimeIndex
-    ) -> TimedeltaIndex: ...
+        self, other: timedelta | np.timedelta64 | np_ndarray_td | BaseOffset
+    ) -> Self: ...
     @final
     def to_series(
         self, index: Index | None = None, name: Hashable | None = None
diff --git a/pandas-stubs/core/indexes/timedeltas.pyi b/pandas-stubs/core/indexes/timedeltas.pyi
index e87592dc8..b15b9afe1 100644
--- a/pandas-stubs/core/indexes/timedeltas.pyi
+++ b/pandas-stubs/core/indexes/timedeltas.pyi
@@ -27,6 +27,10 @@ from pandas._libs.tslibs import BaseOffset
 from pandas._typing import (
     AxesData,
     TimedeltaConvertibleTypes,
+    np_ndarray_anyint,
+    np_ndarray_bool,
+    np_ndarray_dt,
+    np_ndarray_float,
     np_ndarray_td,
     num,
 )
@@ -64,9 +68,42 @@ class TimedeltaIndex(
         self, other: dt.timedelta | Self
     ) -> Self: ...
     def __sub__(  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
-        self, other: dt.timedelta | np.timedelta64 | np_ndarray_td | Self
+        self, other: dt.timedelta | np.timedelta64 | np_ndarray_td | BaseOffset | Self
+    ) -> Self: ...
+    @overload  # type: ignore[override]
+    def __rsub__(
+        self, other: dt.timedelta | np.timedelta64 | np_ndarray_td | BaseOffset | Self
+    ) -> Self: ...
+    @overload
+    def __rsub__(  # pyright: ignore[reportIncompatibleMethodOverride]
+        self, other: dt.datetime | np.datetime64 | np_ndarray_dt | DatetimeIndex
+    ) -> DatetimeIndex: ...
+    def __mul__(  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
+        self,
+        other: (  # type: ignore[override]
+            float
+            | Sequence[float]
+            | np_ndarray_bool
+            | np_ndarray_anyint
+            | np_ndarray_float
+            | Index[bool]
+            | Index[int]
+            | Index[float]
+        ),
+    ) -> Self: ...
+    def __rmul__(  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
+        self,
+        other: (  # type: ignore[override]
+            float
+            | Sequence[float]
+            | np_ndarray_bool
+            | np_ndarray_anyint
+            | np_ndarray_float
+            | Index[bool]
+            | Index[int]
+            | Index[float]
+        ),
     ) -> Self: ...
-    def __mul__(self, other: float) -> Self: ...  # type: ignore[override]  # pyright: ignore[reportIncompatibleMethodOverride]
     @overload  # type: ignore[override]
     def __truediv__(self, other: float | Sequence[float]) -> Self: ...
     @overload
diff --git a/pandas-stubs/core/series.pyi b/pandas-stubs/core/series.pyi
index 04b7a712f..519ad56e9 100644
--- a/pandas-stubs/core/series.pyi
+++ b/pandas-stubs/core/series.pyi
@@ -36,7 +36,9 @@ from typing import (
 from _typeshed import (
     SupportsAdd,
     SupportsGetItem,
+    SupportsMul,
     SupportsRAdd,
+    SupportsRMul,
 )
 from matplotlib.axes import (
     Axes as PlotAxes,
@@ -112,6 +114,7 @@ from pandas._libs.tslibs.offsets import DateOffset
 from pandas._typing import (
     S1,
     S1_CO,
+    S1_CO_NSDT,
     S1_CT,
     S1_CT_NDT,
     S2,
@@ -2533,85 +2536,114 @@ class Series(IndexOpsMixin[S1], NDFrame):
     @overload
     def __mul__(self, other: Index[Never] | Series[Never]) -> Series: ...
     @overload
-    def __mul__(
-        self: Series[bool],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
-    ) -> Series[T_COMPLEX]: ...
+    def __mul__(self, other: np_ndarray_dt) -> Never: ...
     @overload
-    def __mul__(self: Series[bool], other: np_ndarray_bool) -> Series[bool]: ...
+    def __mul__(
+        self: Series[bool] | Series[int] | Series[float],
+        other: (
+            timedelta
+            | Sequence[timedelta]
+            | np.timedelta64
+            | np_ndarray_td
+            | TimedeltaIndex
+            | Series[Timedelta]
+        ),
+    ) -> Series[Timedelta]: ...
     @overload
-    def __mul__(self: Series[bool], other: np_ndarray_anyint) -> Series[int]: ...
+    def __mul__(self: Series[Timestamp], other: np_ndarray) -> Never: ...
     @overload
-    def __mul__(self: Series[bool], other: np_ndarray_float) -> Series[float]: ...
+    def __mul__(self: Series[Timedelta], other: np_ndarray_complex) -> Never: ...
     @overload
     def __mul__(
-        self: Series[int],
+        self: Series[Timedelta],
         other: (
-            bool
-            | Sequence[bool]
+            float
+            | Sequence[float]
             | np_ndarray_bool
             | np_ndarray_anyint
+            | np_ndarray_float
             | Index[bool]
+            | Index[int]
+            | Index[float]
             | Series[bool]
+            | Series[int]
+            | Series[float]
         ),
-    ) -> Series[int]: ...
+    ) -> Series[Timedelta]: ...
     @overload
-    def __mul__(
-        self: Series[int],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
-    ) -> Series[T_COMPLEX]: ...
+    def __mul__(self: Series[T_INT], other: bool | Sequence[bool]) -> Series[T_INT]: ...
     @overload
-    def __mul__(self: Series[int], other: np_ndarray_float) -> Series[float]: ...
+    def __mul__(self: Series[float], other: int | Sequence[int]) -> Series[float]: ...
     @overload
     def __mul__(
-        self: Series[float],
+        self: Series[complex], other: float | Sequence[float]
+    ) -> Series[complex]: ...
+    @overload
+    def __mul__(
+        self: Series[S1_CT],
         other: (
-            int
-            | Sequence[int]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[T_INT]
-            | Series[T_INT]
+            SupportsRMul[S1_CT, S1_CO_NSDT] | Sequence[SupportsRMul[S1_CT, S1_CO_NSDT]]
         ),
-    ) -> Series[float]: ...
+    ) -> Series[S1_CO_NSDT]: ...
     @overload
     def __mul__(
-        self: Series[float],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[T_COMPLEX], other: np_ndarray_bool | Index[bool] | Series[bool]
     ) -> Series[T_COMPLEX]: ...
     @overload
     def __mul__(
-        self: Series[complex],
-        other: (
-            T_COMPLEX
-            | Sequence[T_COMPLEX]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[T_COMPLEX]
-            | Series[T_COMPLEX]
-        ),
-    ) -> Series[complex]: ...
+        self: Series[bool], other: np_ndarray_anyint | Index[int] | Series[int]
+    ) -> Series[int]: ...
     @overload
     def __mul__(
-        self: Series[T_COMPLEX], other: np_ndarray_complex
-    ) -> Series[complex]: ...
+        self: Series[T_COMPLEX], other: np_ndarray_anyint | Index[int] | Series[int]
+    ) -> Series[T_COMPLEX]: ...
+    @overload
+    def __mul__(
+        self: Series[bool] | Series[int],
+        other: np_ndarray_float | Index[float] | Series[float],
+    ) -> Series[float]: ...
     @overload
     def __mul__(
+        self: Series[T_COMPLEX], other: np_ndarray_float | Index[float] | Series[float]
+    ) -> Series[T_COMPLEX]: ...
+    @overload
+    def __mul__(
+        self: Series[T_COMPLEX],
+        other: np_ndarray_complex | Index[complex] | Series[complex],
+    ) -> Series[complex]: ...
+    @overload
+    def mul(
+        self: Series[Never],
+        other: complex | _ListLike | Index | Series,
+        level: Level | None = None,
+        fill_value: float | None = None,
+        axis: int = 0,
+    ) -> Series: ...
+    @overload
+    def mul(
+        self,
+        other: Index[Never] | Series[Never],
+        level: Level | None = None,
+        fill_value: float | None = None,
+        axis: int = 0,
+    ) -> Series: ...
+    @overload
+    def mul(
         self: Series[bool] | Series[int] | Series[float],
         other: (
             timedelta
+            | Sequence[timedelta]
             | np.timedelta64
             | np_ndarray_td
             | TimedeltaIndex
             | Series[Timedelta]
         ),
+        level: Level | None = ...,
+        fill_value: float | None = None,
+        axis: AxisIndex | None = 0,
     ) -> Series[Timedelta]: ...
     @overload
-    def __mul__(self: Series[Timedelta], other: np_ndarray_complex) -> Never: ...
-    @overload
-    def __mul__(
+    def mul(
         self: Series[Timedelta],
         other: (
             float
@@ -2626,136 +2658,102 @@ class Series(IndexOpsMixin[S1], NDFrame):
             | Series[int]
             | Series[float]
         ),
+        level: Level | None = ...,
+        fill_value: float | None = None,
+        axis: AxisIndex | None = 0,
     ) -> Series[Timedelta]: ...
     @overload
     def mul(
-        self: Series[Never],
-        other: complex | _ListLike | Index | Series,
+        self: Series[T_INT],
+        other: bool | Sequence[bool],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series: ...
+    ) -> Series[T_INT]: ...
     @overload
     def mul(
-        self,
-        other: Index[Never] | Series[Never],
+        self: Series[float],
+        other: int | Sequence[int],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series: ...
+    ) -> Series[float]: ...
     @overload
     def mul(
-        self: Series[bool],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[complex],
+        other: float | Sequence[float],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series[T_COMPLEX]: ...
+    ) -> Series[complex]: ...
     @overload
     def mul(
-        self: Series[bool],
-        other: np_ndarray_bool,
+        self: Series[S1_CT],
+        other: (
+            SupportsRMul[S1_CT, S1_CO_NSDT] | Sequence[SupportsRMul[S1_CT, S1_CO_NSDT]]
+        ),
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series[bool]: ...
+    ) -> Series[S1_CO_NSDT]: ...
     @overload
     def mul(
-        self: Series[bool],
-        other: np_ndarray_anyint,
+        self: Series[T_COMPLEX],
+        other: np_ndarray_bool | Index[bool] | Series[bool],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series[int]: ...
+    ) -> Series[T_COMPLEX]: ...
     @overload
     def mul(
         self: Series[bool],
-        other: np_ndarray_float,
-        level: Level | None = None,
-        fill_value: float | None = None,
-        axis: int = 0,
-    ) -> Series[float]: ...
-    @overload
-    def mul(
-        self: Series[int],
-        other: (
-            bool
-            | Sequence[bool]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | Index[bool]
-            | Series[bool]
-        ),
+        other: np_ndarray_anyint | Index[int] | Series[int],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[int]: ...
     @overload
     def mul(
-        self: Series[int],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[T_COMPLEX],
+        other: np_ndarray_anyint | Index[int] | Series[int],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[T_COMPLEX]: ...
     @overload
     def mul(
-        self: Series[int],
-        other: np_ndarray_float,
-        level: Level | None = None,
-        fill_value: float | None = None,
-        axis: int = 0,
-    ) -> Series[float]: ...
-    @overload
-    def mul(
-        self: Series[float],
-        other: (
-            int
-            | Sequence[int]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[T_INT]
-            | Series[T_INT]
-        ),
+        self: Series[bool] | Series[int],
+        other: np_ndarray_float | Index[float] | Series[float],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[float]: ...
     @overload
     def mul(
-        self: Series[float],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[T_COMPLEX],
+        other: np_ndarray_float | Index[float] | Series[float],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[T_COMPLEX]: ...
     @overload
-    def mul(
-        self: Series[complex],
-        other: (
-            T_COMPLEX
-            | Sequence[T_COMPLEX]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[T_COMPLEX]
-            | Series[T_COMPLEX]
-        ),
-        level: Level | None = None,
-        fill_value: float | None = None,
-        axis: int = 0,
-    ) -> Series[complex]: ...
-    @overload
     def mul(
         self: Series[T_COMPLEX],
-        other: np_ndarray_complex,
+        other: np_ndarray_complex | Index[complex] | Series[complex],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[complex]: ...
     @overload
-    def mul(
+    def __rmul__(  # type: ignore[overload-overlap]
+        self: Series[Never], other: complex | NumListLike | Index | Series
+    ) -> Series: ...
+    @overload
+    def __rmul__(self, other: Index[Never] | Series[Never]) -> Series: ...  # type: ignore[misc]
+    @overload
+    def __rmul__(self, other: np_ndarray_dt) -> Never: ...
+    @overload
+    def __rmul__(
         self: Series[bool] | Series[int] | Series[float],
         other: (
             timedelta
@@ -2765,12 +2763,13 @@ class Series(IndexOpsMixin[S1], NDFrame):
             | TimedeltaIndex
             | Series[Timedelta]
         ),
-        level: Level | None = ...,
-        fill_value: float | None = None,
-        axis: AxisIndex | None = 0,
     ) -> Series[Timedelta]: ...
     @overload
-    def mul(
+    def __rmul__(self: Series[Timestamp], other: np_ndarray) -> Never: ...
+    @overload
+    def __rmul__(self: Series[Timedelta], other: np_ndarray_complex) -> Never: ...
+    @overload
+    def __rmul__(
         self: Series[Timedelta],
         other: (
             float
@@ -2785,96 +2784,83 @@ class Series(IndexOpsMixin[S1], NDFrame):
             | Series[int]
             | Series[float]
         ),
-        level: Level | None = ...,
-        fill_value: float | None = None,
-        axis: AxisIndex | None = 0,
     ) -> Series[Timedelta]: ...
     @overload
-    def __rmul__(  # type: ignore[overload-overlap]
-        self: Series[Never], other: complex | NumListLike | Index | Series
-    ) -> Series: ...
-    @overload
-    def __rmul__(self, other: Index[Never] | Series[Never]) -> Series: ...
-    @overload
     def __rmul__(
-        self: Series[bool],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
-    ) -> Series[T_COMPLEX]: ...
-    @overload
-    def __rmul__(self: Series[bool], other: np_ndarray_bool) -> Series[bool]: ...
+        self: Series[T_INT], other: bool | Sequence[bool]
+    ) -> Series[T_INT]: ...
     @overload
-    def __rmul__(self: Series[bool], other: np_ndarray_anyint) -> Series[int]: ...
+    def __rmul__(self: Series[float], other: int | Sequence[int]) -> Series[float]: ...
     @overload
-    def __rmul__(self: Series[bool], other: np_ndarray_float) -> Series[float]: ...
+    def __rmul__(
+        self: Series[complex], other: float | Sequence[float]
+    ) -> Series[complex]: ...
     @overload
     def __rmul__(
-        self: Series[int],
+        self: Series[S1_CT],
         other: (
-            bool
-            | Sequence[bool]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | Index[bool]
-            | Series[bool]
+            SupportsMul[S1_CT, S1_CO_NSDT] | Sequence[SupportsMul[S1_CT, S1_CO_NSDT]]
         ),
-    ) -> Series[int]: ...
+    ) -> Series[S1_CO_NSDT]: ...
     @overload
     def __rmul__(
-        self: Series[int],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[T_COMPLEX], other: np_ndarray_bool | Index[bool] | Series[bool]
     ) -> Series[T_COMPLEX]: ...
     @overload
-    def __rmul__(self: Series[int], other: np_ndarray_float) -> Series[float]: ...
+    def __rmul__(
+        self: Series[bool], other: np_ndarray_anyint | Index[int] | Series[int]
+    ) -> Series[int]: ...
+    @overload
+    def __rmul__(
+        self: Series[T_COMPLEX], other: np_ndarray_anyint | Index[int] | Series[int]
+    ) -> Series[T_COMPLEX]: ...
     @overload
     def __rmul__(
-        self: Series[float],
-        other: (
-            int
-            | Sequence[int]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[T_INT]
-            | Series[T_INT]
-        ),
+        self: Series[bool] | Series[int],
+        other: np_ndarray_float | Index[float] | Series[float],
     ) -> Series[float]: ...
     @overload
     def __rmul__(
-        self: Series[float],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[T_COMPLEX], other: np_ndarray_float | Index[float] | Series[float]
     ) -> Series[T_COMPLEX]: ...
     @overload
     def __rmul__(
-        self: Series[complex],
-        other: (
-            T_COMPLEX
-            | Sequence[T_COMPLEX]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[T_COMPLEX]
-            | Series[T_COMPLEX]
-        ),
+        self: Series[T_COMPLEX],
+        other: np_ndarray_complex | Index[complex] | Series[complex],
     ) -> Series[complex]: ...
     @overload
-    def __rmul__(
-        self: Series[T_COMPLEX], other: np_ndarray_complex
-    ) -> Series[complex]: ...
+    def rmul(
+        self: Series[Never],
+        other: complex | _ListLike | Index | Series,
+        level: Level | None = None,
+        fill_value: float | None = None,
+        axis: int = 0,
+    ) -> Series: ...
     @overload
-    def __rmul__(
+    def rmul(
+        self,
+        other: Index[Never] | Series[Never],
+        level: Level | None = None,
+        fill_value: float | None = None,
+        axis: int = 0,
+    ) -> Series: ...
+    @overload
+    def rmul(
         self: Series[bool] | Series[int] | Series[float],
         other: (
             timedelta
+            | Sequence[timedelta]
             | np.timedelta64
             | np_ndarray_td
             | TimedeltaIndex
             | Series[Timedelta]
         ),
+        level: Level | None = ...,
+        fill_value: float | None = None,
+        axis: AxisIndex | None = 0,
     ) -> Series[Timedelta]: ...
     @overload
-    def __rmul__(self: Series[Timedelta], other: np_ndarray_complex) -> Never: ...
-    @overload
-    def __rmul__(
+    def rmul(
         self: Series[Timedelta],
         other: (
             float
@@ -2889,169 +2875,92 @@ class Series(IndexOpsMixin[S1], NDFrame):
             | Series[int]
             | Series[float]
         ),
+        level: Level | None = ...,
+        fill_value: float | None = None,
+        axis: AxisIndex | None = 0,
     ) -> Series[Timedelta]: ...
     @overload
     def rmul(
-        self: Series[Never],
-        other: complex | _ListLike | Index | Series,
+        self: Series[T_INT],
+        other: bool | Sequence[bool],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series: ...
+    ) -> Series[T_INT]: ...
     @overload
     def rmul(
-        self,
-        other: Index[Never] | Series[Never],
+        self: Series[float],
+        other: int | Sequence[int],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series: ...
+    ) -> Series[float]: ...
     @overload
     def rmul(
-        self: Series[bool],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[complex],
+        other: float | Sequence[float],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series[T_COMPLEX]: ...
+    ) -> Series[complex]: ...
     @overload
     def rmul(
-        self: Series[bool],
-        other: np_ndarray_bool,
+        self: Series[S1_CT],
+        other: (
+            SupportsMul[S1_CT, S1_CO_NSDT] | Sequence[SupportsMul[S1_CT, S1_CO_NSDT]]
+        ),
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series[bool]: ...
+    ) -> Series[S1_CO_NSDT]: ...
     @overload
     def rmul(
-        self: Series[bool],
-        other: np_ndarray_anyint,
+        self: Series[T_COMPLEX],
+        other: np_ndarray_bool | Index[bool] | Series[bool],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
-    ) -> Series[int]: ...
+    ) -> Series[T_COMPLEX]: ...
     @overload
     def rmul(
         self: Series[bool],
-        other: np_ndarray_float,
-        level: Level | None = None,
-        fill_value: float | None = None,
-        axis: int = 0,
-    ) -> Series[float]: ...
-    @overload
-    def rmul(
-        self: Series[int],
-        other: (
-            bool
-            | Sequence[bool]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | Index[bool]
-            | Series[bool]
-        ),
+        other: np_ndarray_anyint | Index[int] | Series[int],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[int]: ...
     @overload
     def rmul(
-        self: Series[int],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[T_COMPLEX],
+        other: np_ndarray_anyint | Index[int] | Series[int],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[T_COMPLEX]: ...
     @overload
     def rmul(
-        self: Series[int],
-        other: np_ndarray_float,
-        level: Level | None = None,
-        fill_value: float | None = None,
-        axis: int = 0,
-    ) -> Series[float]: ...
-    @overload
-    def rmul(
-        self: Series[float],
-        other: (
-            int
-            | Sequence[int]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[T_INT]
-            | Series[T_INT]
-        ),
+        self: Series[bool] | Series[int],
+        other: np_ndarray_float | Index[float] | Series[float],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[float]: ...
     @overload
     def rmul(
-        self: Series[float],
-        other: T_COMPLEX | Sequence[T_COMPLEX] | Index[T_COMPLEX] | Series[T_COMPLEX],
+        self: Series[T_COMPLEX],
+        other: np_ndarray_float | Index[float] | Series[float],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[T_COMPLEX]: ...
     @overload
-    def rmul(
-        self: Series[complex],
-        other: (
-            T_COMPLEX
-            | Sequence[T_COMPLEX]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[T_COMPLEX]
-            | Series[T_COMPLEX]
-        ),
-        level: Level | None = None,
-        fill_value: float | None = None,
-        axis: int = 0,
-    ) -> Series[complex]: ...
-    @overload
     def rmul(
         self: Series[T_COMPLEX],
-        other: np_ndarray_complex,
+        other: np_ndarray_complex | Index[complex] | Series[complex],
         level: Level | None = None,
         fill_value: float | None = None,
         axis: int = 0,
     ) -> Series[complex]: ...
-    @overload
-    def rmul(
-        self: Series[bool] | Series[int] | Series[float],
-        other: (
-            timedelta
-            | Sequence[timedelta]
-            | np.timedelta64
-            | np_ndarray_td
-            | TimedeltaIndex
-            | Series[Timedelta]
-        ),
-        level: Level | None = ...,
-        fill_value: float | None = None,
-        axis: AxisIndex | None = 0,
-    ) -> Series[Timedelta]: ...
-    @overload
-    def rmul(
-        self: Series[Timedelta],
-        other: (
-            float
-            | Sequence[float]
-            | np_ndarray_bool
-            | np_ndarray_anyint
-            | np_ndarray_float
-            | Index[bool]
-            | Index[int]
-            | Index[float]
-            | Series[bool]
-            | Series[int]
-            | Series[float]
-        ),
-        level: Level | None = ...,
-        fill_value: float | None = None,
-        axis: AxisIndex | None = 0,
-    ) -> Series[Timedelta]: ...
     def __mod__(self, other: num | _ListLike | Series[S1]) -> Series[S1]: ...
     def __ne__(self, other: object) -> Series[_bool]: ...  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
     def __pow__(self, other: num | _ListLike | Series[S1]) -> Series[S1]: ...
diff --git a/tests/indexes/arithmetic/bool/test_mul.py b/tests/indexes/arithmetic/bool/test_mul.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/indexes/arithmetic/complex/test_mul.py b/tests/indexes/arithmetic/complex/test_mul.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/indexes/arithmetic/datetime/__init__.py b/tests/indexes/arithmetic/datetime/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/indexes/arithmetic/float/test_mul.py b/tests/indexes/arithmetic/float/test_mul.py
new file mode 100644
index 000000000..e3b4fa4e0
--- /dev/null
+++ b/tests/indexes/arithmetic/float/test_mul.py
@@ -0,0 +1,128 @@
+from datetime import (
+    datetime,
+    timedelta,
+)
+from typing import Any
+
+import numpy as np
+from numpy import typing as npt  # noqa: F401
+import pandas as pd
+from typing_extensions import (
+    Never,
+    assert_type,
+)
+
+from tests import (
+    TYPE_CHECKING_INVALID_USAGE,
+    check,
+)
+
+left = pd.Index([1.0, 2.0, 3.0])  # left operand
+
+
+def test_mul_py_scalar() -> None:
+    """Test pd.Index[float] * Python native scalars"""
+    b, i, f, c = True, 1, 1.0, 1j
+    s, d = datetime(2025, 9, 30), timedelta(seconds=1)
+
+    check(assert_type(left * b, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * i, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * f, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * c, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.TimedeltaIndex"), pd.TimedeltaIndex, timedelta)
+
+    check(assert_type(b * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(i * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(f * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(c * left, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.TimedeltaIndex"), pd.TimedeltaIndex, timedelta)
+
+
+def test_mul_py_sequence() -> None:
+    """Test pd.Index[float] * Python native sequences"""
+    b, i, f, c = [True, False, True], [2, 3, 5], [1.0, 2.0, 3.0], [1j, 1j, 4j]
+    s = [datetime(2025, 9, d) for d in (27, 28, 29)]
+    d = [timedelta(seconds=s + 1) for s in range(3)]
+
+    check(assert_type(left * b, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * i, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * f, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * c, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Index[pd.Timedelta]"), pd.Index, timedelta)
+
+    check(assert_type(b * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(i * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(f * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(c * left, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Index[pd.Timedelta]"), pd.Index, timedelta)
+
+
+def test_mul_numpy_array() -> None:
+    """Test pd.Index[float] * numpy arrays"""
+    b = np.array([True, False, True], np.bool_)
+    i = np.array([2, 3, 5], np.int64)
+    f = np.array([1.0, 2.0, 3.0], np.float64)
+    c = np.array([1.1j, 2.2j, 4.1j], np.complex128)
+    s = np.array([np.datetime64(f"2025-09-{d}") for d in (27, 28, 29)], np.datetime64)
+    d = np.array([np.timedelta64(s + 1, "s") for s in range(3)], np.timedelta64)
+
+    check(assert_type(left * b, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * i, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * f, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * c, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type(left * s, Never)
+    check(assert_type(left * d, pd.TimedeltaIndex), pd.TimedeltaIndex, pd.Timedelta)
+
+    # `numpy` typing gives the corresponding `ndarray`s in the static type
+    # checking, where our `__rmul__` cannot override. At runtime, they return
+    # `Series` with the correct element type.
+    check(assert_type(b * left, "npt.NDArray[np.bool_]"), pd.Index, np.floating)
+    check(assert_type(i * left, "npt.NDArray[np.int64]"), pd.Index, np.floating)
+    check(assert_type(f * left, "npt.NDArray[np.float64]"), pd.Index, np.floating)
+    check(
+        assert_type(c * left, "npt.NDArray[np.complex128]"),
+        pd.Index,
+        np.complexfloating,
+    )
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type(s * left, Any)
+    check(
+        assert_type(d * left, "npt.NDArray[np.timedelta64]"),
+        pd.TimedeltaIndex,
+        pd.Timedelta,
+    )
+
+
+def test_mul_pd_index() -> None:
+    """Test pd.Index[float] * pandas Indexes"""
+    b = pd.Index([True, False, True])
+    i = pd.Index([2, 3, 5])
+    f = pd.Index([1.0, 2.0, 3.0])
+    c = pd.Index([1.1j, 2.2j, 4.1j])
+    s = pd.Index([datetime(2025, 9, d) for d in (27, 28, 29)])
+    d = pd.Index([timedelta(seconds=s + 1) for s in range(3)])
+
+    check(assert_type(left * b, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * i, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * f, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * c, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, pd.TimedeltaIndex), pd.TimedeltaIndex, pd.Timedelta)
+
+    check(assert_type(b * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(i * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(f * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(c * left, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, pd.TimedeltaIndex), pd.TimedeltaIndex, pd.Timedelta)
diff --git a/tests/indexes/arithmetic/int/test_mul.py b/tests/indexes/arithmetic/int/test_mul.py
new file mode 100644
index 000000000..1f0a395c7
--- /dev/null
+++ b/tests/indexes/arithmetic/int/test_mul.py
@@ -0,0 +1,126 @@
+from datetime import (
+    datetime,
+    timedelta,
+)
+from typing import Any
+
+import numpy as np
+from numpy import typing as npt  # noqa: F401
+import pandas as pd
+from typing_extensions import (
+    Never,
+    assert_type,
+)
+
+from tests import (
+    TYPE_CHECKING_INVALID_USAGE,
+    check,
+)
+
+left = pd.Index([1, 2, 3])  # left operand
+
+
+def test_mul_py_scalar() -> None:
+    """Test pd.Index[int] * Python native scalars"""
+    b, i, f, c = True, 1, 1.0, 1j
+    s, d = datetime(2025, 9, 27), timedelta(seconds=1)
+
+    check(assert_type(left * b, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(left * i, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(left * f, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * c, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, pd.TimedeltaIndex), pd.Index, pd.Timedelta)
+
+    check(assert_type(b * left, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(i * left, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(f * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(c * left, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, pd.TimedeltaIndex), pd.Index, pd.Timedelta)
+
+
+def test_mul_py_sequence() -> None:
+    """Test pd.Index[int] * Python native sequences"""
+    b, i, f, c = [True, False, True], [2, 3, 5], [1.0, 2.0, 3.0], [1j, 1j, 4j]
+    s = [datetime(2025, 9, d) for d in (27, 28, 29)]
+    d = [timedelta(seconds=s + 1) for s in range(3)]
+
+    check(assert_type(left * b, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(left * i, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(left * f, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * c, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    # pandas-dev/pandas#62524
+    check(assert_type(left * d, "pd.Index[pd.Timedelta]"), pd.Index, timedelta)
+
+    check(assert_type(b * left, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(i * left, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(f * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(c * left, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    # pandas-dev/pandas#62524
+    check(assert_type(d * left, "pd.Index[pd.Timedelta]"), pd.Index, timedelta)
+
+
+def test_mul_numpy_array() -> None:
+    """Test pd.Index[int] * numpy arrays"""
+    b = np.array([True, False, True], np.bool_)
+    i = np.array([2, 3, 5], np.int64)
+    f = np.array([1.0, 2.0, 3.0], np.float64)
+    c = np.array([1.1j, 2.2j, 4.1j], np.complex128)
+    s = np.array([np.datetime64(f"2025-09-{d}") for d in (27, 28, 29)], np.datetime64)
+    d = np.array([np.timedelta64(s + 1, "s") for s in range(3)], np.timedelta64)
+
+    check(assert_type(left * b, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(left * i, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(left * f, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * c, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type(left * s, Never)
+    check(assert_type(left * d, pd.TimedeltaIndex), pd.Index, pd.Timedelta)
+
+    # `numpy` typing gives the corresponding `ndarray`s in the static type
+    # checking, where our `__rmul__` cannot override. At runtime, they return
+    # `Series` with the correct element type.
+    check(assert_type(b * left, "npt.NDArray[np.bool_]"), pd.Index, np.integer)
+    check(assert_type(i * left, "npt.NDArray[np.int64]"), pd.Index, np.integer)
+    check(assert_type(f * left, "npt.NDArray[np.float64]"), pd.Index, np.floating)
+    check(
+        assert_type(c * left, "npt.NDArray[np.complex128]"),
+        pd.Index,
+        np.complexfloating,
+    )
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type(s * left, Any)
+    check(assert_type(d * left, "npt.NDArray[np.timedelta64]"), pd.Index, pd.Timedelta)
+
+
+def test_mul_pd_index() -> None:
+    """Test pd.Index[int] * pandas Indexes"""
+    b = pd.Index([True, False, True])
+    i = pd.Index([2, 3, 5])
+    f = pd.Index([1.0, 2.0, 3.0])
+    c = pd.Index([1.1j, 2.2j, 4.1j])
+    s = pd.Index([datetime(2025, 9, d) for d in (27, 28, 29)])
+    d = pd.Index([timedelta(seconds=s + 1) for s in range(3)])
+
+    check(assert_type(left * b, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(left * i, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(left * f, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(left * c, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, pd.TimedeltaIndex), pd.Index, pd.Timedelta)
+
+    check(assert_type(b * left, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(i * left, "pd.Index[int]"), pd.Index, np.integer)
+    check(assert_type(f * left, "pd.Index[float]"), pd.Index, np.floating)
+    check(assert_type(c * left, "pd.Index[complex]"), pd.Index, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, pd.TimedeltaIndex), pd.Index, pd.Timedelta)
diff --git a/tests/indexes/arithmetic/test_mul.py b/tests/indexes/arithmetic/test_mul.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/indexes/arithmetic/timedelta/__init__.py b/tests/indexes/arithmetic/timedelta/__init__.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/indexes/arithmetic/timedelta/test_mul.py b/tests/indexes/arithmetic/timedelta/test_mul.py
new file mode 100644
index 000000000..e69de29bb
diff --git a/tests/scalars/test_scalars.py b/tests/scalars/test_scalars.py
index 54fcb08c5..75332fdb0 100644
--- a/tests/scalars/test_scalars.py
+++ b/tests/scalars/test_scalars.py
@@ -519,7 +519,6 @@ def test_timedelta_add_sub() -> None:
     as_dt_timedelta = dt.timedelta(days=1)
     as_timedelta64 = np.timedelta64(1, "D")
     as_timedelta_index = pd.TimedeltaIndex([td])
-    as_timedelta_series = pd.Series(as_timedelta_index)
     as_period_index = pd.period_range("2012-01-01", periods=3, freq="D")
     as_datetime_index = pd.date_range("2012-01-01", periods=3)
     as_ndarray_td64 = ndarray_td64
@@ -535,11 +534,6 @@ def test_timedelta_add_sub() -> None:
     check(assert_type(td + as_dt_timedelta, pd.Timedelta), pd.Timedelta)
     check(assert_type(td + as_timedelta64, pd.Timedelta), pd.Timedelta)
     check(assert_type(td + as_timedelta_index, pd.TimedeltaIndex), pd.TimedeltaIndex)
-    check(
-        assert_type(td + as_timedelta_series, "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
     check(assert_type(td + as_period_index, pd.PeriodIndex), pd.PeriodIndex)
     check(assert_type(td + as_datetime_index, pd.DatetimeIndex), pd.DatetimeIndex)
     check(
@@ -577,11 +571,6 @@ def test_timedelta_add_sub() -> None:
         pd.Timedelta,
     )
     check(assert_type(as_timedelta_index + td, pd.TimedeltaIndex), pd.TimedeltaIndex)
-    check(
-        assert_type(as_timedelta_series + td, "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
     check(assert_type(as_period_index + td, pd.PeriodIndex), pd.PeriodIndex)
     check(assert_type(as_datetime_index + td, pd.DatetimeIndex), pd.DatetimeIndex)
     check(
@@ -612,11 +601,6 @@ def test_timedelta_add_sub() -> None:
     check(assert_type(td - as_dt_timedelta, pd.Timedelta), pd.Timedelta)
     check(assert_type(td - as_timedelta64, pd.Timedelta), pd.Timedelta)
     check(assert_type(td - as_timedelta_index, pd.TimedeltaIndex), pd.TimedeltaIndex)
-    check(
-        assert_type(td - as_timedelta_series, "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
     check(
         assert_type(td - as_ndarray_td64, npt.NDArray[np.timedelta64]),
         np.ndarray,
@@ -646,11 +630,6 @@ def test_timedelta_add_sub() -> None:
         pd.Timedelta,
     )
     check(assert_type(as_timedelta_index - td, pd.TimedeltaIndex), pd.TimedeltaIndex)
-    check(
-        assert_type(as_timedelta_series - td, "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
     check(assert_type(as_period_index - td, pd.PeriodIndex), pd.PeriodIndex)
     check(assert_type(as_datetime_index - td, pd.DatetimeIndex), pd.DatetimeIndex)
     check(
@@ -703,18 +682,6 @@ def test_timedelta_mul_div() -> None:
         np.ndarray,
         np.timedelta64,
     )
-    check(
-        assert_type(td * mp_series_int, "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
-    check(
-        assert_type(td * md_series_float, "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
-    check(assert_type(td * md_int64_index, pd.TimedeltaIndex), pd.TimedeltaIndex)
-    check(assert_type(td * md_float_index, pd.TimedeltaIndex), pd.TimedeltaIndex)
 
     check(assert_type(md_int * td, pd.Timedelta), pd.Timedelta)
     check(assert_type(md_float * td, pd.Timedelta), pd.Timedelta)
@@ -728,18 +695,6 @@ def test_timedelta_mul_div() -> None:
         np.ndarray,
         np.timedelta64,
     )
-    check(
-        assert_type(mp_series_int * td, "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
-    check(
-        assert_type(md_series_float * td, "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
-    check(assert_type(md_int64_index * td, pd.TimedeltaIndex), pd.TimedeltaIndex)
-    check(assert_type(md_float_index * td, pd.TimedeltaIndex), pd.TimedeltaIndex)
 
     check(assert_type(td // td, int), int)
     check(assert_type(td // pd.NaT, float), float)
diff --git a/tests/series/arithmetic/float/test_mul.py b/tests/series/arithmetic/float/test_mul.py
index f4afe08d2..d9d3c71f4 100644
--- a/tests/series/arithmetic/float/test_mul.py
+++ b/tests/series/arithmetic/float/test_mul.py
@@ -1,9 +1,21 @@
+from datetime import (
+    datetime,
+    timedelta,
+)
+from typing import Any
+
 import numpy as np
 from numpy import typing as npt  # noqa: F401
 import pandas as pd
-from typing_extensions import assert_type
+from typing_extensions import (
+    Never,
+    assert_type,
+)
 
-from tests import check
+from tests import (
+    TYPE_CHECKING_INVALID_USAGE,
+    check,
+)
 
 left = pd.Series([1.0, 2.0, 3.0])  # left operand
 
@@ -11,21 +23,31 @@
 def test_mul_py_scalar() -> None:
     """Test pd.Series[float] * Python native scalars"""
     b, i, f, c = True, 1, 1.0, 1j
+    s, d = datetime(2025, 9, 30), timedelta(seconds=1)
 
     check(assert_type(left * b, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * i, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(b * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(i * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(f * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(c * left, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(i), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[call-overload] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.rmul(i), "pd.Series[float]"), pd.Series, np.floating)
@@ -33,26 +55,40 @@ def test_mul_py_scalar() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[call-overload] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
 
 def test_mul_py_sequence() -> None:
     """Test pd.Series[float] * Python native sequences"""
     b, i, f, c = [True, False, True], [2, 3, 5], [1.0, 2.0, 3.0], [1j, 1j, 4j]
+    s = [datetime(2025, 9, d) for d in (27, 28, 29)]
+    d = [timedelta(seconds=s + 1) for s in range(3)]
 
     check(assert_type(left * b, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * i, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(b * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(i * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(f * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(c * left, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(i), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.rmul(i), "pd.Series[float]"), pd.Series, np.floating)
@@ -60,6 +96,9 @@ def test_mul_py_sequence() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
 
 def test_mul_numpy_array() -> None:
@@ -68,11 +107,16 @@ def test_mul_numpy_array() -> None:
     i = np.array([2, 3, 5], np.int64)
     f = np.array([1.0, 2.0, 3.0], np.float64)
     c = np.array([1.1j, 2.2j, 4.1j], np.complex128)
+    s = np.array([np.datetime64(f"2025-09-{d}") for d in (27, 28, 29)], np.datetime64)
+    d = np.array([np.timedelta64(s + 1, "s") for s in range(3)], np.timedelta64)
 
     check(assert_type(left * b, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * i, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type(left * s, Never)
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     # `numpy` typing gives the corresponding `ndarray`s in the static type
     # checking, where our `__rmul__` cannot override. At runtime, they return
@@ -85,11 +129,17 @@ def test_mul_numpy_array() -> None:
         pd.Series,
         np.complexfloating,
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type(s * left, Any)
+    check(assert_type(d * left, "npt.NDArray[np.timedelta64]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(i), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.rmul(i), "pd.Series[float]"), pd.Series, np.floating)
@@ -97,6 +147,9 @@ def test_mul_numpy_array() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
 
 def test_mul_pd_index() -> None:
@@ -105,21 +158,32 @@ def test_mul_pd_index() -> None:
     i = pd.Index([2, 3, 5])
     f = pd.Index([1.0, 2.0, 3.0])
     c = pd.Index([1.1j, 2.2j, 4.1j])
+    s = pd.Index([datetime(2025, 9, d) for d in (27, 28, 29)])
+    d = pd.Index([timedelta(seconds=s + 1) for s in range(3)])
 
     check(assert_type(left * b, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * i, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(b * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(i * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(f * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(c * left, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(i), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.rmul(i), "pd.Series[float]"), pd.Series, np.floating)
@@ -127,6 +191,9 @@ def test_mul_pd_index() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
 
 def test_mul_pd_series() -> None:
@@ -135,21 +202,32 @@ def test_mul_pd_series() -> None:
     i = pd.Series([2, 3, 5])
     f = pd.Series([1.0, 2.0, 3.0])
     c = pd.Series([1.1j, 2.2j, 4.1j])
+    s = pd.Series([datetime(2025, 9, d) for d in (27, 28, 29)])
+    d = pd.Series([timedelta(seconds=s + 1) for s in range(3)])
 
     check(assert_type(left * b, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * i, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(b * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(i * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(f * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(c * left, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(i), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.rmul(i), "pd.Series[float]"), pd.Series, np.floating)
@@ -157,3 +235,6 @@ def test_mul_pd_series() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
diff --git a/tests/series/arithmetic/int/test_mul.py b/tests/series/arithmetic/int/test_mul.py
index b15d91256..548b9ade1 100644
--- a/tests/series/arithmetic/int/test_mul.py
+++ b/tests/series/arithmetic/int/test_mul.py
@@ -1,9 +1,21 @@
+from datetime import (
+    datetime,
+    timedelta,
+)
+from typing import Any
+
 import numpy as np
 from numpy import typing as npt  # noqa: F401
 import pandas as pd
-from typing_extensions import assert_type
+from typing_extensions import (
+    Never,
+    assert_type,
+)
 
-from tests import check
+from tests import (
+    TYPE_CHECKING_INVALID_USAGE,
+    check,
+)
 
 left = pd.Series([1, 2, 3])  # left operand
 
@@ -11,21 +23,31 @@
 def test_mul_py_scalar() -> None:
     """Test pd.Series[int] * Python native scalars"""
     b, i, f, c = True, 1, 1.0, 1j
+    s, d = datetime(2025, 9, 27), timedelta(seconds=1)
 
     check(assert_type(left * b, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * i, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(b * left, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(i * left, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(f * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(c * left, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(i), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[call-overload] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.rmul(i), "pd.Series[int]"), pd.Series, np.integer)
@@ -33,26 +55,40 @@ def test_mul_py_scalar() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[call-overload] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
 
 def test_mul_py_sequence() -> None:
     """Test pd.Series[int] * Python native sequences"""
     b, i, f, c = [True, False, True], [2, 3, 5], [1.0, 2.0, 3.0], [1j, 1j, 4j]
+    s = [datetime(2025, 9, d) for d in (27, 28, 29)]
+    d = [timedelta(seconds=s + 1) for s in range(3)]
 
     check(assert_type(left * b, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * i, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(b * left, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(i * left, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(f * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(c * left, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(i), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.rmul(i), "pd.Series[int]"), pd.Series, np.integer)
@@ -60,6 +96,9 @@ def test_mul_py_sequence() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, timedelta)
 
 
 def test_mul_numpy_array() -> None:
@@ -68,11 +107,16 @@ def test_mul_numpy_array() -> None:
     i = np.array([2, 3, 5], np.int64)
     f = np.array([1.0, 2.0, 3.0], np.float64)
     c = np.array([1.1j, 2.2j, 4.1j], np.complex128)
+    s = np.array([np.datetime64(f"2025-09-{d}") for d in (27, 28, 29)], np.datetime64)
+    d = np.array([np.timedelta64(s + 1, "s") for s in range(3)], np.timedelta64)
 
     check(assert_type(left * b, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * i, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type(left * s, Never)
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     # `numpy` typing gives the corresponding `ndarray`s in the static type
     # checking, where our `__rmul__` cannot override. At runtime, they return
@@ -85,11 +129,17 @@ def test_mul_numpy_array() -> None:
         pd.Series,
         np.complexfloating,
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        assert_type(s * left, Any)
+    check(assert_type(d * left, "npt.NDArray[np.timedelta64]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(i), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.rmul(i), "pd.Series[int]"), pd.Series, np.integer)
@@ -97,6 +147,9 @@ def test_mul_numpy_array() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
 
 def test_mul_pd_index() -> None:
@@ -105,21 +158,32 @@ def test_mul_pd_index() -> None:
     i = pd.Index([2, 3, 5])
     f = pd.Index([1.0, 2.0, 3.0])
     c = pd.Index([1.1j, 2.2j, 4.1j])
+    s = pd.Index([datetime(2025, 9, d) for d in (27, 28, 29)])
+    d = pd.Index([timedelta(seconds=s + 1) for s in range(3)])
 
     check(assert_type(left * b, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * i, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(b * left, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(i * left, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(f * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(c * left, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(i), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.rmul(i), "pd.Series[int]"), pd.Series, np.integer)
@@ -127,6 +191,9 @@ def test_mul_pd_index() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
 
 def test_mul_pd_series() -> None:
@@ -135,21 +202,32 @@ def test_mul_pd_series() -> None:
     i = pd.Series([2, 3, 5])
     f = pd.Series([1.0, 2.0, 3.0])
     c = pd.Series([1.1j, 2.2j, 4.1j])
+    s = pd.Series([datetime(2025, 9, d) for d in (27, 28, 29)])
+    d = pd.Series([timedelta(seconds=s + 1) for s in range(3)])
 
     check(assert_type(left * b, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * i, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left * f, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left * c, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _05 = left * s  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(left * d, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(b * left, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(i * left, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(f * left, "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(c * left, "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _15 = s * left  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
+    check(assert_type(d * left, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.mul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(i), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.mul(f), "pd.Series[float]"), pd.Series, np.floating)
     check(assert_type(left.mul(c), "pd.Series[complex]"), pd.Series, np.complexfloating)
+    if TYPE_CHECKING_INVALID_USAGE:
+        _25 = left.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.mul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
     check(assert_type(left.rmul(b), "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(left.rmul(i), "pd.Series[int]"), pd.Series, np.integer)
@@ -157,3 +235,6 @@ def test_mul_pd_series() -> None:
     check(
         assert_type(left.rmul(c), "pd.Series[complex]"), pd.Series, np.complexfloating
     )
+    if TYPE_CHECKING_INVALID_USAGE:
+        _35 = left.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+    check(assert_type(left.rmul(d), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
diff --git a/tests/series/arithmetic/test_mul.py b/tests/series/arithmetic/test_mul.py
index f89633416..e95b4e02b 100644
--- a/tests/series/arithmetic/test_mul.py
+++ b/tests/series/arithmetic/test_mul.py
@@ -179,5 +179,5 @@ def test_mul_str_py_str() -> None:
     if TYPE_CHECKING_INVALID_USAGE:
         left_i * s  # type: ignore[operator] # pyright:ignore[reportOperatorIssue]
         s * left_i  # type: ignore[operator] # pyright:ignore[reportOperatorIssue]
-        left_i.mul(s)  # type: ignore[type-var] # pyright: ignore[reportArgumentType,reportCallIssue]
-        left_i.rmul(s)  # type: ignore[type-var] # pyright: ignore[reportArgumentType,reportCallIssue]
+        left_i.mul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
+        left_i.rmul(s)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
diff --git a/tests/series/arithmetic/timedelta/test_mul.py b/tests/series/arithmetic/timedelta/test_mul.py
index 8f83ca19e..107886c86 100644
--- a/tests/series/arithmetic/timedelta/test_mul.py
+++ b/tests/series/arithmetic/timedelta/test_mul.py
@@ -41,7 +41,7 @@ def test_mul_py_scalar() -> None:
     check(assert_type(left.mul(i), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
     check(assert_type(left.mul(f), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
     if TYPE_CHECKING_INVALID_USAGE:
-        left.mul(c)  # type: ignore[call-overload] # pyright: ignore[reportArgumentType,reportCallIssue]
+        left.mul(c)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
 
     if PD_LTE_23:
         check(
@@ -52,7 +52,7 @@ def test_mul_py_scalar() -> None:
     check(assert_type(left.rmul(i), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
     check(assert_type(left.rmul(f), "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
     if TYPE_CHECKING_INVALID_USAGE:
-        left.rmul(c)  # type: ignore[call-overload] # pyright: ignore[reportArgumentType,reportCallIssue]
+        left.rmul(c)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType,reportCallIssue]
 
 
 def test_mul_py_sequence() -> None:
diff --git a/tests/series/test_series.py b/tests/series/test_series.py
index 12c75f50d..09d5499ea 100644
--- a/tests/series/test_series.py
+++ b/tests/series/test_series.py
@@ -3278,30 +3278,6 @@ def test_series_mapping() -> None:
     )
 
 
-def test_timedeltaseries_operators() -> None:
-    series = pd.Series([pd.Timedelta(days=1)])
-    check(
-        assert_type(series + datetime.datetime.now(), "pd.Series[pd.Timestamp]"),
-        pd.Series,
-        pd.Timestamp,
-    )
-    check(
-        assert_type(series + datetime.timedelta(1), "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
-    check(
-        assert_type(datetime.datetime.now() + series, "pd.Series[pd.Timestamp]"),
-        pd.Series,
-        pd.Timestamp,
-    )
-    check(
-        assert_type(series - datetime.timedelta(1), "pd.Series[pd.Timedelta]"),
-        pd.Series,
-        pd.Timedelta,
-    )
-
-
 def test_timestamp_series() -> None:
     series = pd.Series([pd.Timestamp(2024, 4, 4)])
     check(
diff --git a/tests/test_timefuncs.py b/tests/test_timefuncs.py
index 2fdf6a138..8e7395e6d 100644
--- a/tests/test_timefuncs.py
+++ b/tests/test_timefuncs.py
@@ -1,9 +1,6 @@
 from __future__ import annotations
 
 import datetime as dt
-from typing import (
-    Optional,
-)
 
 from dateutil.relativedelta import (
     FR,
@@ -154,7 +151,7 @@ def test_timedelta_arithmetic() -> None:
     check(assert_type(td3 / 10.2, pd.Timedelta), pd.Timedelta)
 
 
-def test_timedelta_series_arithmetic() -> None:
+def test_timedelta_index_arithmetic() -> None:
     tds1 = pd.to_timedelta([2, 3], "minutes")
     td1 = pd.Timedelta("2 days")
     check(assert_type(tds1, pd.TimedeltaIndex), pd.TimedeltaIndex)
@@ -170,7 +167,7 @@ def test_timedelta_float_value() -> None:
     check(assert_type(pd.Timedelta(1.5, "h"), pd.Timedelta), pd.Timedelta)
 
 
-def test_timedelta_series_string() -> None:
+def test_timedelta_index_string() -> None:
     seq_list = ["1 day"]
     check(assert_type(pd.to_timedelta(seq_list), pd.TimedeltaIndex), pd.TimedeltaIndex)
 
@@ -198,19 +195,6 @@ def test_datetimeindex_plus_timedelta() -> None:
         pd.Timestamp,
     )
     dti = pd.to_datetime(["2022-03-08", "2022-03-15"])
-    td_s = pd.to_timedelta(pd.Series([10, 20]), "minutes")
-    dti_td_s = dti + td_s
-    check(
-        assert_type(dti_td_s, "pd.Series[pd.Timestamp]"),
-        pd.Series,
-        pd.Timestamp,
-    )
-    td_dti_s = td_s + dti
-    check(
-        assert_type(td_dti_s, "pd.Series[pd.Timestamp]"),
-        pd.Series,
-        pd.Timestamp,
-    )
     tdi = pd.to_timedelta([10, 20], "minutes")
     dti_tdi_dti = dti + tdi
     check(assert_type(dti_tdi_dti, "pd.DatetimeIndex"), pd.DatetimeIndex)
@@ -233,13 +217,6 @@ def test_datetimeindex_minus_timedelta() -> None:
         pd.Timestamp,
     )
     dti = pd.to_datetime(["2022-03-08", "2022-03-15"])
-    td_s = pd.to_timedelta(pd.Series([10, 20]), "minutes")
-    dti_td_s = dti - td_s
-    check(
-        assert_type(dti_td_s, "pd.Series[pd.Timestamp]"),
-        pd.Series,
-        pd.Timestamp,
-    )
     tdi = pd.to_timedelta([10, 20], "minutes")
     dti_tdi_dti = dti - tdi
     check(assert_type(dti_tdi_dti, "pd.DatetimeIndex"), pd.DatetimeIndex)
@@ -249,7 +226,7 @@ def test_datetimeindex_minus_timedelta() -> None:
     check(assert_type(dti_ts_tdi, pd.TimedeltaIndex), pd.TimedeltaIndex)
 
 
-def test_timestamp_plus_timedelta_series() -> None:
+def test_timestamp_series_construction() -> None:
     check(
         assert_type(
             pd.Series([pd.Timestamp("2022-03-05"), pd.Timestamp("2022-03-06")]),
@@ -258,18 +235,6 @@ def test_timestamp_plus_timedelta_series() -> None:
         pd.Series,
         pd.Timestamp,
     )
-    ts = pd.Timestamp("2022-03-05")
-    td = pd.to_timedelta(pd.Series([10, 20]), "minutes")
-    r3 = td + ts
-    check(assert_type(r3, "pd.Series[pd.Timestamp]"), pd.Series, pd.Timestamp)
-    r4 = ts + td
-    check(assert_type(r4, "pd.Series[pd.Timestamp]"), pd.Series, pd.Timestamp)
-
-
-def test_timedelta_series_mult() -> None:
-    df = pd.DataFrame({"x": [1, 3, 5], "y": [2, 2, 6]})
-    std = (df["x"] < df["y"]) * pd.Timedelta(10, "minutes")
-    check(assert_type(std, "pd.Series[pd.Timedelta]"), pd.Series, pd.Timedelta)
 
 
 def test_timedelta_series_sum() -> None:
@@ -289,19 +254,10 @@ def test_iso_calendar() -> None:
     check(assert_type(dates.isocalendar(), pd.DataFrame), pd.DataFrame)
 
 
-def test_fail_on_adding_two_timestamps() -> None:
-    s1 = pd.Series(pd.to_datetime(["2022-05-01", "2022-06-01"]))
-    s2 = pd.Series(pd.to_datetime(["2022-05-15", "2022-06-15"]))
-    if TYPE_CHECKING_INVALID_USAGE:
-        ssum = s1 + s2  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
-        ts = pd.Timestamp("2022-06-30")
-        tsum = s1 + ts  # type: ignore[operator] # pyright: ignore[reportOperatorIssue]
-
-
 def test_dtindex_tzinfo() -> None:
     # GH 71
     dti = pd.date_range("2000-1-1", periods=10)
-    check(assert_type(dti.tzinfo, Optional[dt.tzinfo]), type(None))
+    check(assert_type(dti.tzinfo, dt.tzinfo | None), type(None))
 
 
 def test_todatetime_fromnumpy() -> None:
@@ -376,8 +332,8 @@ def test_series_dt_accessors() -> None:
     check(assert_type(s0.dt.is_leap_year, "pd.Series[bool]"), pd.Series, np.bool_)
     check(assert_type(s0.dt.daysinmonth, "pd.Series[int]"), pd.Series, np.integer)
     check(assert_type(s0.dt.days_in_month, "pd.Series[int]"), pd.Series, np.integer)
-    check(assert_type(s0.dt.tz, Optional[dt.tzinfo]), type(None))
-    check(assert_type(s0.dt.freq, Optional[str]), str)
+    check(assert_type(s0.dt.tz, dt.tzinfo | None), type(None))
+    check(assert_type(s0.dt.freq, str | None), str)
     check(assert_type(s0.dt.isocalendar(), pd.DataFrame), pd.DataFrame)
     check(
         assert_type(s0.dt.to_period("D"), "pd.Series[pd.Period]"), pd.Series, pd.Period
@@ -448,8 +404,8 @@ def test_series_dt_accessors() -> None:
         pd.Series,
         pd.Timestamp,
     )
-    check(assert_type(s0.dt.tz, Optional[dt.tzinfo]), type(None))
-    check(assert_type(s0_local.dt.tz, Optional[dt.tzinfo]), dt.tzinfo)
+    check(assert_type(s0.dt.tz, dt.tzinfo | None), type(None))
+    check(assert_type(s0_local.dt.tz, dt.tzinfo | None), dt.tzinfo)
     check(
         assert_type(s0.dt.normalize(), "pd.Series[pd.Timestamp]"),
         pd.Series,
@@ -676,8 +632,8 @@ def test_datetimeindex_accessors() -> None:
     check(assert_type(i0.is_leap_year, np_1darray[np.bool]), np_1darray[np.bool])
     check(assert_type(i0.daysinmonth, "pd.Index[int]"), pd.Index, np.int32)
     check(assert_type(i0.days_in_month, "pd.Index[int]"), pd.Index, np.int32)
-    check(assert_type(i0.tz, Optional[dt.tzinfo]), type(None))
-    check(assert_type(i0.freq, Optional[BaseOffset]), BaseOffset)
+    check(assert_type(i0.tz, dt.tzinfo | None), type(None))
+    check(assert_type(i0.freq, BaseOffset | None), BaseOffset)
     check(assert_type(i0.isocalendar(), pd.DataFrame), pd.DataFrame)
     check(assert_type(i0.to_period("D"), pd.PeriodIndex), pd.PeriodIndex, pd.Period)
     check(
@@ -698,7 +654,7 @@ def test_datetimeindex_accessors() -> None:
         assert_type(ilocal.tz_convert(pytz.timezone("US/Pacific")), pd.DatetimeIndex),
         pd.DatetimeIndex,
     )
-    check(assert_type(ilocal.tz, Optional[dt.tzinfo]), dt.tzinfo)
+    check(assert_type(ilocal.tz, dt.tzinfo | None), dt.tzinfo)
     check(assert_type(i0.normalize(), pd.DatetimeIndex), pd.DatetimeIndex, pd.Timestamp)
     check(assert_type(i0.strftime("%Y"), pd.Index), pd.Index, str)
     check(assert_type(i0.round("D"), pd.DatetimeIndex), pd.DatetimeIndex, pd.Timestamp)
@@ -763,7 +719,7 @@ def test_periodindex_accessors() -> None:
     check(assert_type(i0.quarter, "pd.Index[int]"), pd.Index, np.integer)
     check(assert_type(i0.daysinmonth, "pd.Index[int]"), pd.Index, np.integer)
     check(assert_type(i0.days_in_month, "pd.Index[int]"), pd.Index, np.integer)
-    check(assert_type(i0.freq, Optional[BaseOffset]), BaseOffset)
+    check(assert_type(i0.freq, BaseOffset | None), BaseOffset)
     check(assert_type(i0.strftime("%Y"), pd.Index), pd.Index, str)
     check(assert_type(i0.asfreq("D"), pd.PeriodIndex), pd.PeriodIndex, pd.Period)
     check(assert_type(i0.end_time, pd.DatetimeIndex), pd.DatetimeIndex, pd.Timestamp)