diff --git a/pandas-stubs/_typing.pyi b/pandas-stubs/_typing.pyi
index 7b2b0081..f14c393f 100644
--- a/pandas-stubs/_typing.pyi
+++ b/pandas-stubs/_typing.pyi
@@ -847,6 +847,26 @@ S1 = TypeVar("S1", bound=SeriesDType, default=Any)
 S2 = TypeVar("S2", bound=SeriesDType)
 S3 = TypeVar("S3", bound=SeriesDType)
 
+# Constraint, instead of bound
+C2 = TypeVar(
+    "C2",
+    str,
+    bytes,
+    datetime.date,
+    datetime.time,
+    bool,
+    int,
+    float,
+    complex,
+    Dtype,
+    datetime.datetime,  # includes pd.Timestamp
+    datetime.timedelta,  # includes pd.Timedelta
+    Period,
+    Interval,
+    CategoricalDtype,
+    BaseOffset,
+)
+
 IndexingInt: TypeAlias = (
     int | np.int_ | np.integer | np.unsignedinteger | np.signedinteger | np.int8
 )
diff --git a/pandas-stubs/core/indexes/base.pyi b/pandas-stubs/core/indexes/base.pyi
index 4f9ebd44..cea53a64 100644
--- a/pandas-stubs/core/indexes/base.pyi
+++ b/pandas-stubs/core/indexes/base.pyi
@@ -42,6 +42,7 @@ from typing_extensions import (
 
 from pandas._libs.interval import _OrderableT
 from pandas._typing import (
+    C2,
     S1,
     AnyAll,
     AxesData,
@@ -401,7 +402,12 @@ class Index(IndexOpsMixin[S1]):
     ) -> Self: ...
     @overload
     def __getitem__(self, idx: int | tuple[np_ndarray_anyint, ...]) -> S1: ...
-    def append(self, other): ...
+    @overload
+    def append(
+        self: Index[C2], other: Index[C2] | Sequence[Index[C2]]
+    ) -> Index[C2]: ...
+    @overload
+    def append(self, other: Index | Sequence[Index]) -> Index: ...
     def putmask(self, mask, value): ...
     def equals(self, other) -> bool: ...
     @final
diff --git a/pandas-stubs/core/indexes/multi.pyi b/pandas-stubs/core/indexes/multi.pyi
index d313852d..5278d081 100644
--- a/pandas-stubs/core/indexes/multi.pyi
+++ b/pandas-stubs/core/indexes/multi.pyi
@@ -135,7 +135,7 @@ class MultiIndex(Index):
     def take(
         self, indices, axis: int = ..., allow_fill: bool = ..., fill_value=..., **kwargs
     ): ...
-    def append(self, other): ...
+    def append(self, other): ...  # pyrefly: ignore
     def argsort(self, *args, **kwargs): ...
     def repeat(self, repeats, axis=...): ...
     @final
diff --git a/pyproject.toml b/pyproject.toml
index 71400163..d916bfa9 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -39,7 +39,7 @@ mypy = "1.17.0"
 pandas = "2.3.0"
 pyarrow = ">=10.0.1"
 pytest = ">=7.1.2"
-pyright = ">=1.1.400"
+pyright = ">=1.1.403"
 ty = "^0.0.1a8"
 pyrefly = "^0.21.0"
 poethepoet = ">=0.16.5"
diff --git a/tests/test_indexes.py b/tests/test_indexes.py
index b3f566cd..57042c29 100644
--- a/tests/test_indexes.py
+++ b/tests/test_indexes.py
@@ -3,7 +3,9 @@
 import datetime as dt
 from typing import (
     TYPE_CHECKING,
+    Any,
     Union,
+    cast,
 )
 
 import numpy as np
@@ -1028,6 +1030,42 @@ def test_getitem() -> None:
     check(assert_type(i0[[0, 2]], "pd.Index[str]"), pd.Index, str)
 
 
+def test_append_mix() -> None:
+    """Test pd.Index.append with mixed types"""
+    first = pd.Index([1])
+    second = pd.Index(["a"])
+    third = pd.Index([1, "a"])
+    check(assert_type(first.append(second), pd.Index), pd.Index)
+    check(assert_type(first.append([second]), pd.Index), pd.Index)
+
+    check(assert_type(first.append(third), pd.Index), pd.Index)
+    check(assert_type(first.append([third]), pd.Index), pd.Index)
+    check(assert_type(first.append([second, third]), pd.Index), pd.Index)
+
+    check(assert_type(third.append([]), pd.Index), pd.Index)
+    check(assert_type(third.append(cast("list[Index[Any]]", [])), pd.Index), pd.Index)
+    check(assert_type(third.append([first]), pd.Index), pd.Index)
+    check(assert_type(third.append([first, second]), pd.Index), pd.Index)
+
+
+def test_append_int() -> None:
+    """Test pd.Index[int].append"""
+    first = pd.Index([1])
+    second = pd.Index([2])
+    check(assert_type(first.append([]), "pd.Index[int]"), pd.Index, np.int64)
+    check(assert_type(first.append(second), "pd.Index[int]"), pd.Index, np.int64)
+    check(assert_type(first.append([second]), "pd.Index[int]"), pd.Index, np.int64)
+
+
+def test_append_str() -> None:
+    """Test pd.Index[str].append"""
+    first = pd.Index(["str"])
+    second = pd.Index(["rts"])
+    check(assert_type(first.append([]), "pd.Index[str]"), pd.Index, str)
+    check(assert_type(first.append(second), "pd.Index[str]"), pd.Index, str)
+    check(assert_type(first.append([second]), "pd.Index[str]"), pd.Index, str)
+
+
 def test_range_index_range() -> None:
     """Test that pd.RangeIndex can be initialized from range."""
     iri = pd.RangeIndex(range(5))