diff --git a/pandas-stubs/_libs/missing.pyi b/pandas-stubs/_libs/missing.pyi
index 2c948529..c06bf361 100644
--- a/pandas-stubs/_libs/missing.pyi
+++ b/pandas-stubs/_libs/missing.pyi
@@ -1,46 +1,243 @@
+from typing import (
+    Any,
+    Callable,
+    Literal,
+    overload,
+)
+
+from pandas import (
+    Index,
+    Series,
+)
+from pandas.core.arrays.boolean import BooleanArray
 from typing_extensions import Self
 
 class NAType:
-    def __new__(cls, *args, **kwargs) -> Self: ...
+    def __new__(cls, *args: Any, **kwargs: Any) -> Self: ...
     def __format__(self, format_spec: str) -> str: ...
-    def __bool__(self) -> None: ...
     def __hash__(self) -> int: ...
     def __reduce__(self) -> str: ...
-    def __add__(self, other) -> NAType: ...
-    def __radd__(self, other) -> NAType: ...
-    def __sub__(self, other) -> NAType: ...
-    def __rsub__(self, other) -> NAType: ...
-    def __mul__(self, other) -> NAType: ...
-    def __rmul__(self, other) -> NAType: ...
-    def __matmul__(self, other) -> NAType: ...
-    def __rmatmul__(self, other) -> NAType: ...
-    def __truediv__(self, other) -> NAType: ...
-    def __rtruediv__(self, other) -> NAType: ...
-    def __floordiv__(self, other) -> NAType: ...
-    def __rfloordiv__(self, other) -> NAType: ...
-    def __mod__(self, other) -> NAType: ...
-    def __rmod__(self, other) -> NAType: ...
-    def __divmod__(self, other) -> NAType: ...
-    def __rdivmod__(self, other) -> NAType: ...
-    def __eq__(self, other) -> bool: ...
-    def __ne__(self, other) -> bool: ...
-    def __le__(self, other) -> bool: ...
-    def __lt__(self, other) -> bool: ...
-    def __gt__(self, other) -> bool: ...
-    def __ge__(self, other) -> bool: ...
-    def __neg__(self, other) -> NAType: ...
-    def __pos__(self, other) -> NAType: ...
-    def __abs__(self, other) -> NAType: ...
-    def __invert__(self, other) -> NAType: ...
-    def __pow__(self, other) -> NAType: ...
-    def __rpow__(self, other) -> NAType: ...
-    def __and__(self, other) -> NAType | None: ...
-    __rand__ = __and__
-    def __or__(self, other) -> bool | NAType: ...
-    __ror__ = __or__
-    def __xor__(self, other) -> NAType: ...
-    __rxor__ = __xor__
+    @overload
+    def __add__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __add__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __add__(self, other: object, /) -> NAType: ...
+    @overload
+    def __radd__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __radd__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __radd__(self, other: object, /) -> NAType: ...
+    @overload
+    def __sub__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __sub__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __sub__(self, other: object, /) -> NAType: ...
+    @overload
+    def __rsub__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __rsub__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __rsub__(self, other: object, /) -> NAType: ...
+    @overload
+    def __mul__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __mul__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __mul__(self, other: object, /) -> NAType: ...
+    @overload
+    def __rmul__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __rmul__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __rmul__(self, other: object, /) -> NAType: ...
+    def __matmul__(self, other: object, /) -> NAType: ...
+    def __rmatmul__(self, other: object, /) -> NAType: ...
+    @overload
+    def __truediv__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __truediv__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __truediv__(self, other: object, /) -> NAType: ...
+    @overload
+    def __rtruediv__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __rtruediv__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __rtruediv__(self, other: object, /) -> NAType: ...
+    @overload
+    def __floordiv__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __floordiv__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __floordiv__(self, other: object, /) -> NAType: ...
+    @overload
+    def __rfloordiv__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __rfloordiv__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __rfloordiv__(self, other: object, /) -> NAType: ...
+    @overload
+    def __mod__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __mod__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __mod__(self, other: object, /) -> NAType: ...
+    @overload
+    def __rmod__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __rmod__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __rmod__(self, other: object, /) -> NAType: ...
+    @overload
+    def __divmod__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> tuple[Series, Series]: ...
+    @overload
+    def __divmod__(self, other: Index, /) -> tuple[Index, Index]: ...  # type: ignore[overload-overlap]
+    @overload
+    def __divmod__(self, other: object, /) -> tuple[NAType, NAType]: ...
+    @overload
+    def __rdivmod__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> tuple[Series, Series]: ...
+    @overload
+    def __rdivmod__(self, other: Index, /) -> tuple[Index, Index]: ...  # type: ignore[overload-overlap]
+    @overload
+    def __rdivmod__(self, other: object, /) -> tuple[NAType, NAType]: ...
+    @overload  # type: ignore[override]
+    def __eq__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series[bool]: ...
+    @overload
+    def __eq__(self, other: Index, /) -> BooleanArray: ...  # type: ignore[overload-overlap]
+    @overload
+    def __eq__(  # pyright: ignore[reportIncompatibleMethodOverride]
+        self, other: object, /
+    ) -> NAType: ...
+    @overload  # type: ignore[override]
+    def __ne__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series[bool]: ...
+    @overload
+    def __ne__(self, other: Index, /) -> BooleanArray: ...  # type: ignore[overload-overlap]
+    @overload
+    def __ne__(  # pyright: ignore[reportIncompatibleMethodOverride]
+        self, other: object, /
+    ) -> NAType: ...
+    @overload
+    def __le__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series[bool]: ...
+    @overload
+    def __le__(self, other: Index, /) -> BooleanArray: ...  # type: ignore[overload-overlap]
+    @overload
+    def __le__(self, other: object, /) -> NAType: ...
+    @overload
+    def __lt__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series[bool]: ...
+    @overload
+    def __lt__(self, other: Index, /) -> BooleanArray: ...  # type: ignore[overload-overlap]
+    @overload
+    def __lt__(self, other: object, /) -> NAType: ...
+    @overload
+    def __gt__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series[bool]: ...
+    @overload
+    def __gt__(self, other: Index, /) -> BooleanArray: ...  # type: ignore[overload-overlap]
+    @overload
+    def __gt__(self, other: object, /) -> NAType: ...
+    @overload
+    def __ge__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series[bool]: ...
+    @overload
+    def __ge__(self, other: Index, /) -> BooleanArray: ...  # type: ignore[overload-overlap]
+    @overload
+    def __ge__(self, other: object, /) -> NAType: ...
+    def __neg__(self) -> NAType: ...
+    def __pos__(self) -> NAType: ...
+    def __abs__(self) -> NAType: ...
+    def __invert__(self) -> NAType: ...
+    @overload
+    def __pow__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __pow__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __pow__(self, other: object, /) -> NAType: ...
+    @overload
+    def __rpow__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __rpow__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __rpow__(self, other: object, /) -> NAType: ...
+    @overload
+    def __and__(self, other: Literal[False], /) -> Literal[False]: ...  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+    @overload
+    def __and__(self, other: bool | NAType, /) -> NAType: ...
+    @overload
+    def __rand__(self, other: Literal[False], /) -> Literal[False]: ...  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+    @overload
+    def __rand__(self, other: bool, /) -> NAType: ...
+    @overload
+    def __or__(self, other: Literal[True], /) -> Literal[True]: ...  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+    @overload
+    def __or__(self, other: bool | NAType, /) -> NAType: ...
+    @overload
+    def __ror__(self, other: Literal[True], /) -> Literal[True]: ...  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+    @overload
+    def __ror__(self, other: bool | NAType, /) -> NAType: ...
+    @overload
+    def __xor__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __xor__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __xor__(self, other: object, /) -> NAType: ...
+    @overload
+    def __rxor__(  # type: ignore[overload-overlap] #  pyright: ignore[reportOverlappingOverload]
+        self, other: Series, /
+    ) -> Series: ...
+    @overload
+    def __rxor__(self, other: Index, /) -> Index: ...  # type: ignore[overload-overlap]
+    @overload
+    def __rxor__(self, other: object, /) -> NAType: ...
     __array_priority__: int
-    def __array_ufunc__(self, ufunc, method, *inputs, **kwargs): ...
+    def __array_ufunc__(
+        self, ufunc: Callable[..., Any], method: str, *inputs: Any, **kwargs: Any
+    ) -> Any: ...
 
 NA: NAType = ...
diff --git a/tests/test_natype.py b/tests/test_natype.py
new file mode 100644
index 00000000..1d80c185
--- /dev/null
+++ b/tests/test_natype.py
@@ -0,0 +1,186 @@
+from typing import (
+    Literal,
+)
+
+import pandas as pd
+from pandas.api.typing import NAType
+from pandas.core.arrays.boolean import BooleanArray
+from typing_extensions import assert_type
+
+from tests import check
+
+
+def test_arithmetic() -> None:
+    na = pd.NA
+
+    s_int = pd.Series([1, 2, 3], dtype="Int64")
+    idx_int: pd.Index[int] = pd.Index([1, 2, 3], dtype="Int64")
+
+    # __add__
+    check(assert_type(na + s_int, pd.Series), pd.Series)
+    check(assert_type(na + idx_int, pd.Index), pd.Index)
+    check(assert_type(na + 1, NAType), NAType)
+
+    # __radd__
+    check(assert_type(s_int + na, pd.Series), pd.Series)
+    # requires orthogonal fix: https://github.com/pandas-dev/pandas-stubs/issues/1347
+    # check(assert_type(idx_int + na, pd.Index), pd.Index)
+    check(assert_type(1 + na, NAType), NAType)
+
+    # __sub__
+    check(assert_type(na - s_int, pd.Series), pd.Series)
+    check(assert_type(na - idx_int, pd.Index), pd.Index)
+    check(assert_type(na - 1, NAType), NAType)
+
+    # __rsub__
+    check(assert_type(s_int - na, pd.Series), pd.Series)
+    # requires orthogonal fix: https://github.com/pandas-dev/pandas-stubs/issues/1347
+    # check(assert_type(idx_int - na, pd.Index), pd.Index)
+    check(assert_type(1 - na, NAType), NAType)
+
+    # __mul__
+    check(assert_type(na * s_int, pd.Series), pd.Series)
+    check(assert_type(na * idx_int, pd.Index), pd.Index)
+    check(assert_type(na * 1, NAType), NAType)
+
+    # __rmul__
+    check(assert_type(s_int * na, pd.Series), pd.Series)
+    # requires orthogonal fix: https://github.com/pandas-dev/pandas-stubs/issues/1347
+    # check(assert_type(idx_int * na, pd.Index), pd.Index)
+    check(assert_type(1 * na, NAType), NAType)
+
+    # __matmul__
+    check(assert_type(na @ 1, NAType), NAType)
+
+    # __rmatmul__
+    check(assert_type(1 @ na, NAType), NAType)
+
+    # __truediv__
+    check(assert_type(na / s_int, pd.Series), pd.Series)
+    check(assert_type(na / idx_int, pd.Index), pd.Index)
+    check(assert_type(na / 1, NAType), NAType)
+
+    # __rtruediv__
+    check(assert_type(s_int / na, pd.Series), pd.Series)
+    check(assert_type(idx_int / na, pd.Index), pd.Index)
+    check(assert_type(1 / na, NAType), NAType)
+
+    # __floordiv__
+    check(assert_type(na // s_int, pd.Series), pd.Series)
+    check(assert_type(na // idx_int, pd.Index), pd.Index)
+    check(assert_type(na // 1, NAType), NAType)
+
+    # __rfloordiv__
+    check(assert_type(s_int // na, pd.Series), pd.Series)
+    check(assert_type(idx_int // na, pd.Index), pd.Index)
+    check(assert_type(1 // na, NAType), NAType)
+
+    # __mod__
+    check(assert_type(na % s_int, pd.Series), pd.Series)
+    check(assert_type(na % idx_int, pd.Index), pd.Index)
+    check(assert_type(na % 1, NAType), NAType)
+
+    # __rmod__
+    check(assert_type(s_int % na, pd.Series), pd.Series)
+    # requires orthogonal fix: https://github.com/pandas-dev/pandas-stubs/issues/1347
+    # check(assert_type(idx_int % na, pd.Index), pd.Index)
+    check(assert_type(1 % na, NAType), NAType)
+
+    # __divmod__
+    # bug upstream: https://github.com/pandas-dev/pandas/issues/62196
+    # check(
+    #     assert_type(
+    #         divmod(na, s_int),
+    #         tuple[pd.Series, pd.Series],
+    #     ),
+    #     tuple,
+    # )
+    # check(
+    #     assert_type(
+    #         # pyright bug: https://github.com/microsoft/pyright/issues/10849, will
+    #         # require `pyright: ignore[reportAssertTypeFailure]` until fixed.
+    #         divmod(na, idx_int),
+    #         tuple[pd.Index, pd.Index],
+    #     ),
+    #     tuple,
+    # )
+    check(assert_type(divmod(na, 1), tuple[NAType, NAType]), tuple)
+
+    # __rdivmod__
+    # bug upstream: https://github.com/pandas-dev/pandas/issues/62196
+    # check(
+    #     assert_type(divmod(s_int, na), tuple[pd.Series, pd.Series]),
+    #     tuple,
+    # )
+    # https://github.com/pandas-dev/pandas-stubs/issues/1347
+    # check(
+    #     assert_type(divmod(idx_int, na), tuple[pd.Index, pd.Index]),
+    #     tuple,
+    # )
+    check(assert_type(divmod(1, na), tuple[NAType, NAType]), tuple)
+
+    # __eq__
+    check(assert_type(na == s_int, "pd.Series[bool]"), pd.Series)
+    check(assert_type(na == idx_int, BooleanArray), BooleanArray)
+    check(assert_type(na == 1, NAType), NAType)
+
+    # __ne__
+    check(assert_type(na != s_int, "pd.Series[bool]"), pd.Series)
+    check(assert_type(na != idx_int, BooleanArray), BooleanArray)
+    check(assert_type(na != 1, NAType), NAType)
+
+    # __le__
+    check(assert_type(na <= s_int, "pd.Series[bool]"), pd.Series)
+    check(assert_type(na <= idx_int, BooleanArray), BooleanArray)
+    check(assert_type(na <= 1, NAType), NAType)
+
+    # __lt__
+    check(assert_type(na < s_int, "pd.Series[bool]"), pd.Series)
+    check(assert_type(na < idx_int, BooleanArray), BooleanArray)
+    check(assert_type(na < 1, NAType), NAType)
+
+    # __gt__
+    check(assert_type(na > s_int, "pd.Series[bool]"), pd.Series)
+    check(assert_type(na > idx_int, BooleanArray), BooleanArray)
+    check(assert_type(na > 1, NAType), NAType)
+
+    # __ge__
+    check(assert_type(na >= s_int, "pd.Series[bool]"), pd.Series)
+    check(assert_type(na >= idx_int, BooleanArray), BooleanArray)
+    check(assert_type(na >= 1, NAType), NAType)
+
+    # __pow__
+    check(assert_type(na**s_int, pd.Series), pd.Series)
+    check(assert_type(na**idx_int, pd.Index), pd.Index)
+    check(assert_type(na**2, NAType), NAType)
+
+    # __rpow__
+    check(assert_type(s_int**na, pd.Series), pd.Series)
+    # requires orthogonal fix: https://github.com/pandas-dev/pandas-stubs/issues/1347
+    # check(assert_type(idx_int**na, pd.Index), pd.Index)
+    check(assert_type(2**na, NAType), NAType)
+
+    # __and__
+    check(assert_type(na & False, Literal[False]), bool)
+    check(assert_type(na & True, NAType), NAType)
+    check(assert_type(na & na, NAType), NAType)
+
+    # __rand__
+    check(assert_type(False & na, Literal[False]), bool)
+    check(assert_type(True & na, NAType), NAType)
+
+    # __or__
+    check(assert_type(na | False, NAType), NAType)
+    check(assert_type(na | True, Literal[True]), bool)
+
+    # __ror__
+    check(assert_type(False | na, NAType), NAType)
+    check(assert_type(True | na, Literal[True]), bool)
+
+    # __xor__
+    check(assert_type(na ^ s_int, pd.Series), pd.Series)
+    check(assert_type(na ^ idx_int, pd.Index), pd.Index)
+
+    # rxor
+    check(assert_type(s_int ^ na, pd.Series), pd.Series)
+    check(assert_type(idx_int ^ na, pd.Index), pd.Index)