diff --git a/scipy-stubs/special/_logsumexp.pyi b/scipy-stubs/special/_logsumexp.pyi
index 71f1748a..c0f45318 100644
--- a/scipy-stubs/special/_logsumexp.pyi
+++ b/scipy-stubs/special/_logsumexp.pyi
@@ -1,50 +1,98 @@
-from typing import Literal, overload
+from typing import overload
 
 import numpy as np
 import optype.numpy as onp
+from scipy._typing import AnyShape, Falsy, Truthy
 
 __all__ = ["log_softmax", "logsumexp", "softmax"]
 
-# TODO: Support `return_sign=True`
 @overload
 def logsumexp(
     a: onp.ToFloat,
-    axis: int | tuple[int, ...] | None = None,
+    axis: AnyShape | None = None,
     b: onp.ToFloat | None = None,
     keepdims: bool = False,
-    return_sign: Literal[False, 0] = False,
+    return_sign: Falsy = False,
 ) -> np.float64: ...
 @overload
 def logsumexp(
     a: onp.ToComplex,
-    axis: int | tuple[int, ...] | None = None,
+    axis: AnyShape | None = None,
     b: onp.ToFloat | None = None,
     keepdims: bool = False,
-    return_sign: Literal[False, 0] = False,
+    return_sign: Falsy = False,
 ) -> np.float64 | np.complex128: ...
 @overload
 def logsumexp(
     a: onp.ToFloatND,
-    axis: int | tuple[int, ...],
+    axis: AnyShape,
     b: onp.ToFloat | onp.ToFloatND | None = None,
     keepdims: bool = False,
-    return_sign: Literal[False, 0] = False,
+    return_sign: Falsy = False,
 ) -> np.float64 | onp.ArrayND[np.float64]: ...
 @overload
 def logsumexp(
     a: onp.ToComplexND,
-    axis: int | tuple[int, ...],
+    axis: AnyShape,
     b: onp.ToFloat | onp.ToFloatND | None = None,
     keepdims: bool = False,
-    return_sign: Literal[False, 0] = False,
+    return_sign: Falsy = False,
 ) -> np.float64 | np.complex128 | onp.ArrayND[np.float64 | np.complex128]: ...
+@overload
+def logsumexp(
+    a: onp.ToFloat,
+    axis: AnyShape | None = None,
+    b: onp.ToFloat | None = None,
+    keepdims: bool = False,
+    *,
+    return_sign: Truthy,
+) -> tuple[np.float64, bool | np.bool_]: ...
+@overload
+def logsumexp(
+    a: onp.ToComplex,
+    axis: AnyShape | None = None,
+    b: onp.ToFloat | None = None,
+    keepdims: bool = False,
+    *,
+    return_sign: Truthy,
+) -> tuple[np.float64 | np.complex128, bool | np.bool_]: ...
+@overload
+def logsumexp(
+    a: onp.ToFloatND,
+    axis: AnyShape,
+    b: onp.ToFloat | onp.ToFloatND | None = None,
+    keepdims: bool = False,
+    *,
+    return_sign: Truthy,
+) -> tuple[np.float64, bool | np.bool_] | tuple[onp.ArrayND[np.float64], onp.ArrayND[np.bool_]]: ...
+@overload
+def logsumexp(
+    a: onp.ToComplexND,
+    axis: AnyShape,
+    b: onp.ToFloat | onp.ToFloatND | None = None,
+    keepdims: bool = False,
+    *,
+    return_sign: Truthy,
+) -> (
+    tuple[np.float64 | np.complex128, bool | np.bool_] | tuple[onp.ArrayND[np.float64 | np.complex128], onp.ArrayND[np.bool_]]
+): ...
 
-# TODO: Overload real/complex and scalar/array
-def softmax(
-    x: onp.ToComplex | onp.ToComplexND,
-    axis: int | tuple[int, ...] | None = None,
-) -> np.float64 | np.complex128 | onp.ArrayND[np.float64 | np.complex128]: ...
-def log_softmax(
-    x: onp.ToComplex | onp.ToComplexND,
-    axis: int | tuple[int, ...] | None = None,
-) -> np.float64 | np.complex128 | onp.ArrayND[np.float64 | np.complex128]: ...
+#
+@overload
+def softmax(x: onp.ToFloat, axis: AnyShape | None = None) -> np.float64: ...
+@overload
+def softmax(x: onp.ToFloatND, axis: AnyShape | None = None) -> onp.ArrayND[np.float64]: ...
+@overload
+def softmax(x: onp.ToComplex, axis: AnyShape | None = None) -> np.float64 | np.complex128: ...
+@overload
+def softmax(x: onp.ToComplexND, axis: AnyShape | None = None) -> onp.ArrayND[np.float64 | np.complex128]: ...
+
+#
+@overload
+def log_softmax(x: onp.ToFloat, axis: AnyShape | None = None) -> np.float64: ...
+@overload
+def log_softmax(x: onp.ToFloatND, axis: AnyShape | None = None) -> onp.ArrayND[np.float64]: ...
+@overload
+def log_softmax(x: onp.ToComplex, axis: AnyShape | None = None) -> np.float64 | np.complex128: ...
+@overload
+def log_softmax(x: onp.ToComplexND, axis: AnyShape | None = None) -> onp.ArrayND[np.float64 | np.complex128]: ...