diff --git a/pandas-stubs/core/indexes/base.pyi b/pandas-stubs/core/indexes/base.pyi
index 3f3332940..35a610cf4 100644
--- a/pandas-stubs/core/indexes/base.pyi
+++ b/pandas-stubs/core/indexes/base.pyi
@@ -626,7 +626,7 @@ class Index(IndexOpsMixin[S1], ElementOpsMixin[S1]):
     def __lt__(self, other: Self | S1) -> np_1darray_bool: ...  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
     def __gt__(self, other: Self | S1) -> np_1darray_bool: ...  # type: ignore[override] # pyright: ignore[reportIncompatibleMethodOverride]
     @overload
-    def __add__(self: Index[Never], other: _str) -> Never: ...
+    def __add__(self: Index[Never], other: _str) -> Index[_str]: ...
     @overload
     def __add__(
         self: Index[Never], other: complex | ArrayLike | SequenceNotStr[S1] | Index
@@ -680,7 +680,7 @@ class Index(IndexOpsMixin[S1], ElementOpsMixin[S1]):
         self: Index[_str], other: np_ndarray_str | Index[_str]
     ) -> Index[_str]: ...
     @overload
-    def __radd__(self: Index[Never], other: _str) -> Never: ...
+    def __radd__(self: Index[Never], other: _str) -> Index[_str]: ...
     @overload
     def __radd__(
         self: Index[Never], other: complex | ArrayLike | SequenceNotStr[S1] | Index
diff --git a/pandas-stubs/core/reshape/pivot.pyi b/pandas-stubs/core/reshape/pivot.pyi
index eb7d9d479..2af85c5f8 100644
--- a/pandas-stubs/core/reshape/pivot.pyi
+++ b/pandas-stubs/core/reshape/pivot.pyi
@@ -67,11 +67,13 @@ _Values: TypeAlias = SequenceNotStr[Any] | _ExtendedAnyArrayLike
 @overload
 def pivot_table(
     data: DataFrame,
-    values: _PivotTableValuesTypes[
+    values: _PivotTableValuesTypes[  # ty: ignore[non-subscriptable]
         Hashable  # ty: ignore[invalid-type-arguments]
     ] = None,
-    index: _PivotTableIndexTypes[Hashable] = None,  # ty: ignore[invalid-type-arguments]
-    columns: _PivotTableColumnsTypes[
+    index: _PivotTableIndexTypes[  # ty: ignore[non-subscriptable]
+        Hashable  # ty: ignore[invalid-type-arguments]
+    ] = None,
+    columns: _PivotTableColumnsTypes[  # ty: ignore[non-subscriptable]
         Hashable  # ty: ignore[invalid-type-arguments]
     ] = None,
     aggfunc: (
@@ -91,13 +93,15 @@ def pivot_table(
 @overload
 def pivot_table(
     data: DataFrame,
-    values: _PivotTableValuesTypes[
+    values: _PivotTableValuesTypes[  # ty: ignore[non-subscriptable]
         Hashable  # ty: ignore[invalid-type-arguments]
     ] = None,
     *,
     index: Grouper,
     columns: (
-        _PivotTableColumnsTypes[Hashable]  # ty: ignore[invalid-type-arguments]
+        _PivotTableColumnsTypes[  # ty: ignore[non-subscriptable]
+            Hashable  # ty: ignore[invalid-type-arguments]
+        ]
         | np_ndarray
         | Index[Any]
     ) = None,
@@ -116,11 +120,13 @@ def pivot_table(
 @overload
 def pivot_table(
     data: DataFrame,
-    values: _PivotTableValuesTypes[
+    values: _PivotTableValuesTypes[  # ty: ignore[non-subscriptable]
         Hashable  # ty: ignore[invalid-type-arguments]
     ] = None,
     index: (
-        _PivotTableIndexTypes[Hashable]  # ty: ignore[invalid-type-arguments]
+        _PivotTableIndexTypes[  # ty: ignore[non-subscriptable]
+            Hashable  # ty: ignore[invalid-type-arguments]
+        ]
         | np_ndarray
         | Index[Any]
     ) = None,
diff --git a/pandas-stubs/core/series.pyi b/pandas-stubs/core/series.pyi
index 469d44ea0..b8326903c 100644
--- a/pandas-stubs/core/series.pyi
+++ b/pandas-stubs/core/series.pyi
@@ -1789,6 +1789,8 @@ class Series(IndexOpsMixin[S1], ElementOpsMixin[S1], NDFrame):
     # just failed to generate these so I couldn't match
     # them up.
     @overload
+    def __add__(self: Series[Never], other: _str) -> Series[_str]: ...
+    @overload
     def __add__(self: Series[Never], other: complex | ListLike) -> Series: ...
     @overload
     def __add__(self, other: Index[Never] | Series[Never]) -> Series: ...
@@ -2008,6 +2010,8 @@ class Series(IndexOpsMixin[S1], ElementOpsMixin[S1], NDFrame):
         axis: int = 0,
     ) -> Series[_str]: ...
     @overload
+    def __radd__(self: Series[Never], other: _str) -> Series[_str]: ...
+    @overload
     def __radd__(self: Series[Never], other: complex | ListLike) -> Series: ...
     @overload
     def __radd__(self, other: Index[Never] | Series[Never]) -> Series: ...
diff --git a/tests/indexes/arithmetic/test_add.py b/tests/indexes/arithmetic/test_add.py
index c7c415b46..1316e8830 100644
--- a/tests/indexes/arithmetic/test_add.py
+++ b/tests/indexes/arithmetic/test_add.py
@@ -3,7 +3,6 @@
 import numpy as np
 import pandas as pd
 from typing_extensions import (
-    Never,
     assert_type,
 )
 
@@ -107,5 +106,6 @@ def test_add_i_py_str() -> None:
     s = "abc"
 
     if TYPE_CHECKING_INVALID_USAGE:
-        assert_type(left_i + s, Never)
-        assert_type(s + left_i, Never)
+        # relaxing typing, won't work at runtime though
+        assert_type(left_i + s, "pd.Index[str]")
+        assert_type(s + left_i, "pd.Index[str]")
diff --git a/tests/series/arithmetic/str/test_add.py b/tests/series/arithmetic/str/test_add.py
index 6aa5ce0ff..355d277b3 100644
--- a/tests/series/arithmetic/str/test_add.py
+++ b/tests/series/arithmetic/str/test_add.py
@@ -145,3 +145,12 @@ def test_add_pd_series() -> None:
     if TYPE_CHECKING_INVALID_USAGE:
         left.radd(i)  # type: ignore[arg-type] # pyright: ignore[reportArgumentType, reportCallIssue]
     check(assert_type(left.radd(r0), "pd.Series[str]"), pd.Series, str)
+
+
+def test_series_add_str() -> None:
+    """Test Series.__add__ with Series[Any]."""
+    df = pd.DataFrame({0: ["a", "b"]})
+    sr = df[0]
+
+    check(assert_type(sr + "c1", "pd.Series[str]"), pd.Series, str)
+    check(assert_type("c1" + sr, "pd.Series[str]"), pd.Series, str)
diff --git a/tests/test_timefuncs.py b/tests/test_timefuncs.py
index 0b210feb2..678317728 100644
--- a/tests/test_timefuncs.py
+++ b/tests/test_timefuncs.py
@@ -1,7 +1,9 @@
 from __future__ import annotations
 
 import datetime as dt
-from typing import TypeAlias
+from typing import (
+    TypeAlias,
+)
 
 from dateutil.relativedelta import (
     FR,