diff --git a/pandas-stubs/core/series.pyi b/pandas-stubs/core/series.pyi
index 5ce55142b..562aca141 100644
--- a/pandas-stubs/core/series.pyi
+++ b/pandas-stubs/core/series.pyi
@@ -1111,20 +1111,18 @@ class Series(IndexOpsMixin[S1], ElementOpsMixin[S1], NDFrame):
     @overload
     def map(
         self,
-        arg: Callable[[S1], S2 | NAType] | Mapping[S1, S2] | Series[S2],
-        na_action: Literal["ignore"] = ...,
-    ) -> Series[S2]: ...
-    @overload
-    def map(
-        self,
-        arg: Callable[[S1 | NAType], S2 | NAType] | Mapping[S1, S2] | Series[S2],
-        na_action: None = None,
+        arg: (
+            Callable[[S1], S2 | None | NAType]
+            | Mapping[S1, S2 | None | NAType]
+            | Series[S2]
+        ),
+        na_action: Literal["ignore"] | None = None,
     ) -> Series[S2]: ...
     @overload
     def map(
         self,
-        arg: Callable[[Any], Any] | Mapping[Any, Any] | Series,
-        na_action: Literal["ignore"] | None = ...,
+        arg: Callable[[Any], object] | Mapping[Any, object] | Series[Any],
+        na_action: Literal["ignore"] | None = None,
     ) -> Series: ...
     @overload
     def aggregate(
diff --git a/tests/series/test_series.py b/tests/series/test_series.py
index 6a41e339b..27ceb35cc 100644
--- a/tests/series/test_series.py
+++ b/tests/series/test_series.py
@@ -3700,6 +3700,7 @@ def test_map() -> None:
         pd.Series,
         str,
     )
+    check(assert_type(s.map(mapping), "pd.Series[str]"), pd.Series, str)
 
     def callable(x: int) -> str:
         return str(x)
@@ -3709,16 +3710,35 @@ def callable(x: int) -> str:
         pd.Series,
         str,
     )
+    check(assert_type(s.map(callable), "pd.Series[str]"), pd.Series, str)
 
     series = pd.Series(["a", "b", "c"])
     check(
         assert_type(s.map(series, na_action="ignore"), "pd.Series[str]"), pd.Series, str
     )
+    check(assert_type(s.map(series), "pd.Series[str]"), pd.Series, str)
 
     unknown_series = pd.Series([1, 0, None])
     check(
-        assert_type(unknown_series.map({1: True, 0: False, None: None}), pd.Series),
+        assert_type(
+            unknown_series.map({1: True, 0: False, None: None}), "pd.Series[bool]"
+        ),
+        pd.Series,
+        bool,
+    )
+    check(
+        assert_type(
+            unknown_series.map({1: True, 0: False, None: None}, na_action="ignore"),
+            "pd.Series[bool]",
+        ),
         pd.Series,
+        bool,
+    )
+    s_mixed = pd.Series([1, "a"])
+    check(
+        assert_type(s_mixed.map({1: 1.0, "a": 2.0}), "pd.Series[float]"),
+        pd.Series,
+        float,
     )
 
 
@@ -3736,10 +3756,22 @@ def callable(x: int | NAType) -> str | NAType:
     check(
         assert_type(s.map(callable, na_action=None), "pd.Series[str]"), pd.Series, str
     )
+    # na_action defaults to None
+    check(assert_type(s.map(callable), "pd.Series[str]"), pd.Series, str)
 
     series = pd.Series(["a", "b", "c"])
     check(assert_type(s.map(series, na_action=None), "pd.Series[str]"), pd.Series, str)
 
+    def callable2(x: int | NAType | None) -> str | None:
+        if isinstance(x, int):
+            return str(x)
+        return None
+
+    check(
+        assert_type(s.map(callable2, na_action=None), "pd.Series[str]"), pd.Series, str
+    )
+    check(assert_type(s.map(callable2), "pd.Series[str]"), pd.Series, str)
+
 
 def test_case_when() -> None:
     c = pd.Series([6, 7, 8, 9], name="c")