@@ -314,17 +314,17 @@
   "314": "Base UI Plus: `BaseTemporal.%s` received %s, which isn't an object of date fields. `with()` replaces the date fields of an object, and keeps the calendar of the date, so it rejects temporal values and objects with a calendar or a time zone. Pass the fields to replace, such as `{ day: 1 }`, and call `withCalendar()` to change the calendar.",
   "315": "Base UI Plus: `BaseTemporal.%s` received no date field the calendar of the date reads. `with()` can't tell which fields to replace. Pass at least one of `year`, `month`, `monthCode` and `day`, or `era` and `eraYear` outside the ISO calendar.",
   "316": "Base UI Plus: A calendar received %s where it expects a `PlainDate`. The calendar reads the year, the month and the day of each date, so it can't use this one. Create dates with `BaseTemporal.PlainDate.from()`. A Server Component sends a `PlainDate` to the client as its string: pass that string to `from()` in a Client Component.",
-  "317": "Base UI Plus: `BaseTemporal.PlainDate.from()` received %s, which isn't an existing date in the `YYYY-MM-DD` format. Other ISO 8601 forms, such as times, offsets, time zone annotations or 6-digit years, are not supported. Pass a date such as `'2024-05-24'`, optionally followed by a calendar annotation such as `'[u-ca=hebrew]'`.",
+  "317": "Base UI Plus: `BaseTemporal.PlainDate.from()` received %s, which isn't an existing date in the `YYYY-MM-DD` or `±YYYYYY-MM-DD` format. Other ISO 8601 forms, such as times, offsets or time zone annotations, are not supported. Pass a date such as `'2024-05-24'`, optionally followed by a calendar annotation such as `'[u-ca=hebrew]'`.",
   "318": "Base UI Plus: `BaseTemporal.PlainDate.from()` received %s, which isn't a date. `from()` can't read a year, a month and a day from it. Pass a `PlainDate`, an object such as `{ year: 2024, month: 5, day: 24 }`, or a string such as `'2024-05-24'`.",
   "319": "Base UI Plus: `BaseTemporal.%s` received date fields that %s. The fields don't name a single date of the calendar. Pass a year (or an era and a year of era), a month (or a month code) and a day that exist in the calendar.",
   "320": "Base UI Plus: `BaseTemporal.%s` received an object without %s. A date can't be built without its year, month and day. Pass an object such as `{ year: 2024, month: 5, day: 24 }`, with an era and a year of era together in place of the year if needed.",
-  "321": "Base UI Plus: `PlainDate` received the year %s, the month %s and the day %s, which don't name a supported date. The year must be from 0 to 9999, the month from 1 to 12, and the day must exist in the month. Pass a valid date, or create it with `BaseTemporal.PlainDate.from()` and an object to move a month or a day above its range to the closest valid value.",
+  "321": "Base UI Plus: `PlainDate` received the year %s, the month %s and the day %s, which don't name a supported date. The month must be from 1 to 12, the day must exist in the month, and the date must be from -271821-04-20 to +275760-09-13, the days of `Date`. Pass a valid date, or create it with `BaseTemporal.PlainDate.from()` and an object to move a month or a day above its range to the closest valid value.",
   "322": "Base UI Plus: A temporal value received %s as its calendar, which isn't a string. Calendars are identified by their name. Pass a calendar identifier such as `'iso8601'`, `'gregory'` or `'hebrew'`.",
   "323": "Base UI Plus: The \"%s\" calendar isn't supported. Base UI Plus has no arithmetic for it, so it cannot create or display its dates. Use `iso8601`, `gregory`, or one of the calendars listed in the documentation.",
   "324": "Base UI Plus: The \"%s\" calendar isn't registered. Only the ISO and Gregorian calendars are built in, so other calendars stay out of the bundles that don't use them. Pass `%sCalendar` to `registerCalendar()`, both from `@base-ui/plus/calendar-systems`, before creating or displaying its dates.",
   "325": "Base UI Plus: `registerCalendar()` received %s, which isn't a calendar of `@base-ui/plus/calendar-systems`. Base UI Plus only registers the calendars it implements. Pass a calendar such as `hebrewCalendar` from `'@base-ui/plus/calendar-systems'`.",
   "326": "Base UI Plus: `registerCalendar()` received a second implementation of the \"%s\" calendar. Two implementations could give different dates for the same values, so the first registration stays. Make sure a single copy of `@base-ui/plus` is installed, and register each calendar once.",
-  "327": "Base UI Plus: A date of the \"%s\" calendar is outside the days it supports, from the ISO date %s-%s-%s to %s-%s-%s. Outside these days, `Intl.DateTimeFormat` doesn't label dates as Base UI Plus computes them, or the ISO year is outside 0 to 9999. Use a date inside the range.",
+  "327": "Base UI Plus: A date of the \"%s\" calendar is outside the days it supports, from the ISO date %s-%s-%s to %s-%s-%s. Outside these days, `Intl.DateTimeFormat` doesn't label dates as Base UI Plus computes them, or `Date` can't represent them. Use a date inside the range.",
   "328": "Base UI Plus: A temporal value received %s as the %s, which isn't a finite number. A temporal value cannot represent a non-finite field. Pass finite numbers for its date and time fields.",
   "329": "Base UI Plus: The options of `BaseTemporal.%s` are %s, which isn't an object. The method can't read the `overflow` option from them. Pass an object such as `{ overflow: 'reject' }`, or no options.",
   "330": "Base UI Plus: The `overflow` option of `BaseTemporal.%s` is %s, which isn't supported. The method can't tell whether to adjust or reject a field above its range. Pass `'constrain'` or `'reject'`.",
@@ -333,6 +333,8 @@
   "333": "Base UI Plus: The time string has an unsupported format. Its clock fields cannot be read. Use HH:mm or HH:mm:ss with up to nine fractional digits.",
   "334": "Base UI Plus: The time has no clock fields. A clock time cannot be created. Pass a string such as '09:30' or an object such as { hour: 9, minute: 30 }.",
   "335": "Base UI Plus: The %s of the time is out of range. The clock time cannot be created. Pass an integer between 0 and %s.",
-  "336": "Base UI Plus: The zoned date-time is outside the supported years. Fields cannot display it. Use a date-time between years 0 and 9999.",
-  "337": "Base UI Plus: The zoned date-time could not be created or changed. Its date, clock time, offset or timezone could not be resolved: %s. Pass a valid ISO date-time and timezone, and choose a disambiguation policy for skipped or repeated clock times."
+  "336": "Base UI Plus: The zoned date-time is outside the supported range. Like in Temporal, its instant must be one of the instants of `Date`, and its date must be from -271821-04-20 to +275760-09-13. Use a date-time inside this range.",
+  "337": "Base UI Plus: The zoned date-time could not be created or changed. Its date, clock time, offset or timezone could not be resolved: %s. Pass a valid ISO date-time and timezone, and choose a disambiguation policy for skipped or repeated clock times.",
+  "338": "Base UI Plus: `BaseTemporal.%s` received %s, which isn't an object of fields. `with()` replaces the fields of an object, and keeps the calendar of the value, so it rejects temporal values and objects with a calendar or a time zone. Pass only the fields to replace, such as `{ day: 1 }` for a date or `{ hour: 9 }` for a time.",
+  "339": "Base UI Plus: `BaseTemporal.%s` received no field the value reads. `with()` can't tell which fields to replace. Pass at least one field of the value, such as `{ day: 1 }` for a date or `{ hour: 9 }` for a time. Only calendars with eras, unlike the ISO calendar, read `era` and `eraYear`."
 }
@@ -105,47 +105,47 @@ describe('recurring-events/RecurringSeries', () => {
   });
 
   describe('last supported day', () => {
-    it('should end every frequency on December 31, 9999', () => {
-      const lastYear = ['9999-01-01T00:00:00', '9999-12-31T00:00:00'] as const;
+    it('should end every frequency on September 13, 275760', () => {
+      const lastYear = ['+275760-01-01T00:00:00', '+275760-09-13T00:00:00'] as const;
       expect(
         getOccurrenceDays(
           { freq: 'YEARLY' },
-          '9998-06-01T09:00:00',
-          '9998-01-01T00:00:00',
+          '+275759-06-01T09:00:00',
+          '+275759-01-01T00:00:00',
           lastYear[1],
         ),
-      ).to.deep.equal(['9998-06-01', '9999-06-01']);
+      ).to.deep.equal(['+275759-06-01', '+275760-06-01']);
       expect(
-        getOccurrenceDays({ freq: 'DAILY', interval: 300 }, '9999-06-01T09:00:00', ...lastYear),
-      ).to.deep.equal(['9999-06-01']);
+        getOccurrenceDays({ freq: 'DAILY', interval: 300 }, '+275760-06-01T09:00:00', ...lastYear),
+      ).to.deep.equal(['+275760-06-01']);
       expect(
-        getOccurrenceDays({ freq: 'MONTHLY', interval: 5 }, '9999-10-15T09:00:00', ...lastYear),
-      ).to.deep.equal(['9999-10-15']);
+        getOccurrenceDays({ freq: 'MONTHLY', interval: 5 }, '+275760-08-15T09:00:00', ...lastYear),
+      ).to.deep.equal(['+275760-08-15']);
       // The month after the first one is too far to compute.
       expect(
         getOccurrenceDays(
           { freq: 'MONTHLY', interval: Number.MAX_VALUE },
-          '9999-10-15T09:00:00',
+          '+275760-08-15T09:00:00',
           ...lastYear,
         ),
-      ).to.deep.equal(['9999-10-15']);
+      ).to.deep.equal(['+275760-08-15']);
     });
 
-    it('should end the series when its next day of the week or month is in the year 10000', () => {
-      // The Sunday of the last week of 9999 is January 2nd, 10000.
+    it('should end the series when its next day of the week or month is after September 13, 275760', () => {
+      // September 13th, 275760 is a Saturday, so the Sunday of its week is after it.
       expect(
         getOccurrenceDays(
           { freq: 'WEEKLY', byDay: ['SU'] },
-          '9999-12-26T09:00:00',
-          '9999-12-27T00:00:00',
-          '9999-12-31T00:00:00',
+          '+275760-09-07T09:00:00',
+          '+275760-09-08T00:00:00',
+          '+275760-09-13T00:00:00',
         ),
       ).to.deep.equal([]);
-      // December 9999 has no 5th Sunday, which would be January 2nd, 10000.
+      // September 275760 has no 5th Sunday before the 13th, and August 31st is the last one.
       const series = new RecurringSeries(adapter, {
         rule: { freq: 'MONTHLY', byDay: ['5SU'], count: 3 },
-        ...seriesStart(adapter.date('9999-10-31T09:00:00', 'UTC')),
-        exDates: [adapter.date('9999-10-31T09:00:00', 'UTC')],
+        ...seriesStart(adapter.date('+275760-08-31T09:00:00', 'UTC')),
+        exDates: [adapter.date('+275760-08-31T09:00:00', 'UTC')],
       });
       expect(series.hasOccurrence()).to.equal(false);
     });
 
@@ -53,7 +53,7 @@ export declare namespace BaseTemporal {
     readonly eraYear: number | undefined;
     /**
      * The year in the calendar, which keeps counting down before its first era: the ISO year 0 is
-     * 1 BC. ISO years go from 0 to 9999.
+     * 1 BC.
      */
     readonly year: number;
     /**
@@ -81,6 +81,11 @@ export declare namespace BaseTemporal {
      * The number of months in the year.
      */
     readonly monthsInYear: number;
+    /**
+     * A date has no time. Date-times have every other member of a date, so this keeps them out of
+     * the APIs that take a date, such as the date field.
+     */
+    readonly hour?: undefined;
     /**
      * Returns the date moved by a duration in its calendar, like Temporal. Years keep the month
      * code, or move to the month that replaces it in a year without it, and months count the
@@ -208,7 +213,8 @@ export function getWeekDayIndex(dayOfWeek: number, firstDayOfWeek: number): numb
  */
 const UNVALIDATED = Symbol('unvalidated');
 
-const ISO_DATE_REGEXP = /^(\d{4})-(\d{2})-(\d{2})$/;
+// Like in Temporal, a year has four digits, or a sign and six digits, but `-000000` isn't a year.
+const ISO_DATE_REGEXP = /^(\d{4}|\+\d{6}|-(?!0{6})\d{6})-(\d{2})-(\d{2})$/;
 
 /**
  * The units of a Temporal duration, in the order Temporal reads them.
@@ -226,12 +232,10 @@ const DURATION_UNITS = [
   'years',
 ] as const;
 
-const WITH_FIELDS = ['year', 'era', 'eraYear', 'month', 'monthCode', 'day'] as const;
-
 /**
  * More years than the supported days span in any calendar.
  */
-const MAX_YEARS = 20_000;
+const MAX_YEARS = 600_000;
 
 /**
  * Reads a duration like Temporal. Its time units must be 0.
@@ -488,34 +492,9 @@ export class PlainDate implements BaseTemporal.PlainDate {
    */
   public with(fields: PlainDateWithFields, options?: PlainDateFromOptions): PlainDate {
     const apiName = 'PlainDate.prototype.with()';
-    if (
-      typeof fields !== 'object' ||
-      fields === null ||
-      ['calendar', 'calendarId', 'timeZone'].some(
-        (key) => (fields as Record<string, unknown>)[key] !== undefined,
-      )
-    ) {
-      throw new TypeError(
-        `Base UI Plus: \`BaseTemporal.${apiName}\` received ${String(fields)}, which isn't an object of date fields. ` +
-          '`with()` replaces the date fields of an object, and keeps the calendar of the date, so it rejects temporal values and objects with a calendar or a time zone. ' +
-          'Pass the fields to replace, such as `{ day: 1 }`, and call `withCalendar()` to change the calendar.',
-      );
-    }
-    // Like Temporal, a calendar without eras ignores the era fields.
-    const partial: PlainDateWithFields = { ...fields };
-    if (getCalendar(this.calendarId).getYearFromEra == null) {
-      partial.era = undefined;
-      partial.eraYear = undefined;
-    }
-    if (WITH_FIELDS.every((field) => partial[field] === undefined)) {
-      throw new TypeError(
-        `Base UI Plus: \`BaseTemporal.${apiName}\` received no date field the calendar of the date reads. ` +
-          "`with()` can't tell which fields to replace. " +
-          'Pass at least one of `year`, `month`, `monthCode` and `day`, or `era` and `eraYear` outside the ISO calendar.',
-      );
-    }
     return createPlainDate(
-      readDate(mergeDateFields(this, partial), readOverflow(options, apiName), apiName).dayNumber,
+      readDate(mergeDateFields(this, fields, apiName), readOverflow(options, apiName), apiName)
+        .dayNumber,
       this.calendarId,
     );
   }
@@ -611,8 +590,8 @@ export function readDate(
     const day = Number(match?.[3]);
     if (match == null || !isValidIsoDate(year, month, day)) {
       throw new Error(
-        `Base UI Plus: \`BaseTemporal.PlainDate.from()\` received ${JSON.stringify(item)}, which isn't an existing date in the \`YYYY-MM-DD\` format. ` +
-          'Other ISO 8601 forms, such as times, offsets, time zone annotations or 6-digit years, are not supported. ' +
+        `Base UI Plus: \`BaseTemporal.PlainDate.from()\` received ${JSON.stringify(item)}, which isn't an existing date in the \`YYYY-MM-DD\` or \`±YYYYYY-MM-DD\` format. ` +
+          'Other ISO 8601 forms, such as times, offsets or time zone annotations, are not supported. ' +
           "Pass a date such as `'2024-05-24'`, optionally followed by a calendar annotation such as `'[u-ca=hebrew]'`.",
       );
     }
@@ -629,9 +608,17 @@ export function readDate(
     );
   }
   const calendar = getItemCalendar(item);
-  const dayNumber =
-    calendar.resolveFields?.(item, overflow, apiName) ??
-    resolveIsoFields(calendar, item, overflow, apiName);
+  let dayNumber: number;
+  if (typeof (item as Partial<BaseTemporal.PlainDate>).withCalendar === 'function') {
+    // A temporal value, such as a `Temporal` one, whose era codes can differ from the calendar's,
+    // such as `gregory-inverse`: its ISO fields name the same day.
+    const isoDate = (item as BaseTemporal.PlainDate).withCalendar(ISO_CALENDAR_ID);
+    dayNumber = toDayNumber(isoDate.year, isoDate.month, isoDate.day);
+  } else {
+    dayNumber =
+      calendar.resolveFields?.(item, overflow, apiName) ??
+      resolveIsoFields(calendar, item, overflow, apiName);
+  }
   checkCalendarRange(calendar, dayNumber);
   return { dayNumber, calendar };
 }
 
@@ -30,6 +30,11 @@ export interface PlainDateTimeFields extends PlainTimeFields, PlainDateFields {}
 
 export type PlainDateTimeInput = PlainDateTimeFields | string;
 
+/**
+ * The fields `with()` replaces, read in the calendar of the value.
+ */
+export type PlainDateTimeWithFields = Partial<Omit<PlainDateTimeFields, 'calendar'>>;
+
 // Declared apart from the class, like `BaseTemporal.PlainDate`.
 export declare namespace BaseTemporal {
   /**
@@ -61,7 +66,7 @@ export declare namespace BaseTemporal {
      * Returns the date-time with some fields replaced, with the rules of `BaseTemporal.PlainDate`
      * for the date fields.
      */
-    with(fields: Partial<PlainDateTimeFields>, options?: PlainDateFromOptions): PlainDateTime;
+    with(fields: PlainDateTimeWithFields, options?: PlainDateFromOptions): PlainDateTime;
     /**
      * Returns the same date at another time, midnight by default.
      */
@@ -196,7 +201,7 @@ export class PlainDateTime implements BaseTemporal.PlainDateTime {
     let time: Required<PlainTimeFields>;
     if (typeof item === 'string') {
       const annotated = readCalendarAnnotation(item);
-      const match = /^(\d{4}-\d{2}-\d{2})T(.+)$/.exec(annotated.text);
+      const match = /^((?:\d{4}|[+-]\d{6})-\d{2}-\d{2})T(.+)$/.exec(annotated.text);
       if (match == null) {
         throw new Error(
           'Base UI Plus: The date-time string has an unsupported format. ' +
@@ -233,12 +238,8 @@ export class PlainDateTime implements BaseTemporal.PlainDateTime {
     const value = other instanceof PlainDateTime ? other : PlainDateTime.from(other);
     return PlainDateTime.compare(this, value) === 0 && this.calendarId === value.calendarId;
   }
-  with(fields: Partial<PlainDateTimeFields>, options?: PlainDateFromOptions): PlainDateTime {
-    const time: PlainTimeFields = {};
-    for (const key of TIME_FIELDS) {
-      time[key] = fields[key] ?? this[key];
-    }
-    return PlainDateTime.from({ ...mergeDateFields(this.date, fields), ...time }, options);
+  with(fields: PlainDateTimeWithFields, options?: PlainDateFromOptions): PlainDateTime {
+    return withFields(this, fields, options, 'PlainDateTime.prototype.with()', TIME_FIELDS);
   }
   withPlainTime(time: PlainTimeInput = new PlainTime()): PlainDateTime {
     return createPlainDateTime(this.date, readTime(time));
@@ -263,6 +264,25 @@ export class PlainDateTime implements BaseTemporal.PlainDateTime {
   }
 }
 
+/**
+ * Returns `dateTime` with the fields `with()` received replaced. `fieldNames` are the fields of the
+ * value besides its date fields, at least one of which `fields` must set without a date field.
+ */
+export function withFields(
+  dateTime: PlainDateTime,
+  fields: PlainDateTimeWithFields,
+  options: PlainDateFromOptions | undefined,
+  apiName: string,
+  fieldNames: readonly string[],
+): PlainDateTime {
+  const dateFields = mergeDateFields(dateTime.toPlainDate(), fields, apiName, fieldNames);
+  const time: PlainTimeFields = {};
+  for (const key of TIME_FIELDS) {
+    time[key] = fields[key] ?? dateTime[key];
+  }
+  return PlainDateTime.from({ ...dateFields, ...time }, options);
+}
+
 /**
  * Creates a date-time from a date and a time read by `readTime()`, without checking them again.
  */