diff --git a/pandas/_typing.py b/pandas/_typing.py
index 433f8645d35a8..93d49497a85e0 100644
--- a/pandas/_typing.py
+++ b/pandas/_typing.py
@@ -126,10 +126,9 @@
 ]
 
 # dtypes
-NpDtype = Union[str, np.dtype]
-Dtype = Union[
-    "ExtensionDtype", NpDtype, type_t[Union[str, float, int, complex, bool, object]]
-]
+NpDtype = Union[str, np.dtype, type_t[Union[str, float, int, complex, bool, object]]]
+Dtype = Union["ExtensionDtype", NpDtype]
+AstypeArg = Union["ExtensionDtype", "npt.DTypeLike"]
 # DtypeArg specifies all allowable dtypes in a functions its dtype argument
 DtypeArg = Union[Dtype, Dict[Hashable, Dtype]]
 DtypeObj = Union[np.dtype, "ExtensionDtype"]
diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index 4cc0d4185b22c..b0b7b81d059e6 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -18,6 +18,7 @@
     Sequence,
     TypeVar,
     cast,
+    overload,
 )
 
 import numpy as np
@@ -25,6 +26,7 @@
 from pandas._libs import lib
 from pandas._typing import (
     ArrayLike,
+    AstypeArg,
     Dtype,
     FillnaOptions,
     PositionalIndexer,
@@ -520,9 +522,21 @@ def nbytes(self) -> int:
     # Additional Methods
     # ------------------------------------------------------------------------
 
-    def astype(self, dtype, copy=True):
+    @overload
+    def astype(self, dtype: npt.DTypeLike, copy: bool = ...) -> np.ndarray:
+        ...
+
+    @overload
+    def astype(self, dtype: ExtensionDtype, copy: bool = ...) -> ExtensionArray:
+        ...
+
+    @overload
+    def astype(self, dtype: AstypeArg, copy: bool = ...) -> ArrayLike:
+        ...
+
+    def astype(self, dtype: AstypeArg, copy: bool = True) -> ArrayLike:
         """
-        Cast to a NumPy array with 'dtype'.
+        Cast to a NumPy array or ExtensionArray with 'dtype'.
 
         Parameters
         ----------
@@ -535,8 +549,10 @@ def astype(self, dtype, copy=True):
 
         Returns
         -------
-        array : ndarray
-            NumPy ndarray with 'dtype' for its dtype.
+        array : np.ndarray or ExtensionArray
+            An ExtensionArray if dtype is StringDtype,
+            or same as that of underlying array.
+            Otherwise a NumPy ndarray with 'dtype' for its dtype.
         """
         from pandas.core.arrays.string_ import StringDtype
 
@@ -552,7 +568,11 @@ def astype(self, dtype, copy=True):
             # allow conversion to StringArrays
             return dtype.construct_array_type()._from_sequence(self, copy=False)
 
-        return np.array(self, dtype=dtype, copy=copy)
+        # error: Argument "dtype" to "array" has incompatible type
+        # "Union[ExtensionDtype, dtype[Any]]"; expected "Union[dtype[Any], None, type,
+        # _SupportsDType, str, Union[Tuple[Any, int], Tuple[Any, Union[int,
+        # Sequence[int]]], List[Any], _DTypeDict, Tuple[Any, Any]]]"
+        return np.array(self, dtype=dtype, copy=copy)  # type: ignore[arg-type]
 
     def isna(self) -> np.ndarray | ExtensionArraySupportsAnyAll:
         """
@@ -863,6 +883,8 @@ def searchsorted(
         # 2. Values between the values in the `data_for_sorting` fixture
         # 3. Missing values.
         arr = self.astype(object)
+        if isinstance(value, ExtensionArray):
+            value = value.astype(object)
         return arr.searchsorted(value, side=side, sorter=sorter)
 
     def equals(self, other: object) -> bool:
diff --git a/pandas/core/arrays/boolean.py b/pandas/core/arrays/boolean.py
index 14d059c04b7c0..6f473249c9a7e 100644
--- a/pandas/core/arrays/boolean.py
+++ b/pandas/core/arrays/boolean.py
@@ -1,7 +1,10 @@
 from __future__ import annotations
 
 import numbers
-from typing import TYPE_CHECKING
+from typing import (
+    TYPE_CHECKING,
+    overload,
+)
 import warnings
 
 import numpy as np
@@ -12,7 +15,9 @@
 )
 from pandas._typing import (
     ArrayLike,
+    AstypeArg,
     Dtype,
+    npt,
     type_t,
 )
 from pandas.compat.numpy import function as nv
@@ -33,6 +38,7 @@
 from pandas.core.dtypes.missing import isna
 
 from pandas.core import ops
+from pandas.core.arrays import ExtensionArray
 from pandas.core.arrays.masked import (
     BaseMaskedArray,
     BaseMaskedDtype,
@@ -392,7 +398,20 @@ def reconstruct(x):
     def _coerce_to_array(self, value) -> tuple[np.ndarray, np.ndarray]:
         return coerce_to_array(value)
 
-    def astype(self, dtype, copy: bool = True) -> ArrayLike:
+    @overload
+    def astype(self, dtype: npt.DTypeLike, copy: bool = ...) -> np.ndarray:
+        ...
+
+    @overload
+    def astype(self, dtype: ExtensionDtype, copy: bool = ...) -> ExtensionArray:
+        ...
+
+    @overload
+    def astype(self, dtype: AstypeArg, copy: bool = ...) -> ArrayLike:
+        ...
+
+    def astype(self, dtype: AstypeArg, copy: bool = True) -> ArrayLike:
+
         """
         Cast to a NumPy array or ExtensionArray with 'dtype'.
 
diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index c6be9e5886a1d..b8ceef3d52e41 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -11,6 +11,7 @@
     TypeVar,
     Union,
     cast,
+    overload,
 )
 from warnings import (
     catch_warnings,
@@ -32,6 +33,7 @@
 from pandas._libs.lib import no_default
 from pandas._typing import (
     ArrayLike,
+    AstypeArg,
     Dtype,
     NpDtype,
     Ordered,
@@ -482,7 +484,19 @@ def _constructor(self) -> type[Categorical]:
     def _from_sequence(cls, scalars, *, dtype: Dtype | None = None, copy=False):
         return Categorical(scalars, dtype=dtype, copy=copy)
 
-    def astype(self, dtype: Dtype, copy: bool = True) -> ArrayLike:
+    @overload
+    def astype(self, dtype: npt.DTypeLike, copy: bool = ...) -> np.ndarray:
+        ...
+
+    @overload
+    def astype(self, dtype: ExtensionDtype, copy: bool = ...) -> ExtensionArray:
+        ...
+
+    @overload
+    def astype(self, dtype: AstypeArg, copy: bool = ...) -> ArrayLike:
+        ...
+
+    def astype(self, dtype: AstypeArg, copy: bool = True) -> ArrayLike:
         """
         Coerce this type to another dtype
 
@@ -2458,11 +2472,7 @@ def _str_get_dummies(self, sep="|"):
         # sep may not be in categories. Just bail on this.
         from pandas.core.arrays import PandasArray
 
-        # error: Argument 1 to "PandasArray" has incompatible type
-        # "ExtensionArray"; expected "Union[ndarray, PandasArray]"
-        return PandasArray(self.astype(str))._str_get_dummies(  # type: ignore[arg-type]
-            sep
-        )
+        return PandasArray(self.astype(str))._str_get_dummies(sep)
 
 
 # The Series.cat accessor
diff --git a/pandas/core/arrays/floating.py b/pandas/core/arrays/floating.py
index 1acbcf17dfffd..25b4076bd23c6 100644
--- a/pandas/core/arrays/floating.py
+++ b/pandas/core/arrays/floating.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+from typing import overload
 import warnings
 
 import numpy as np
@@ -10,7 +11,9 @@
 )
 from pandas._typing import (
     ArrayLike,
+    AstypeArg,
     DtypeObj,
+    npt,
 )
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import cache_readonly
@@ -31,6 +34,7 @@
 )
 from pandas.core.dtypes.missing import isna
 
+from pandas.core.arrays import ExtensionArray
 from pandas.core.arrays.numeric import (
     NumericArray,
     NumericDtype,
@@ -271,7 +275,19 @@ def _from_sequence_of_strings(
     def _coerce_to_array(self, value) -> tuple[np.ndarray, np.ndarray]:
         return coerce_to_array(value, dtype=self.dtype)
 
-    def astype(self, dtype, copy: bool = True) -> ArrayLike:
+    @overload
+    def astype(self, dtype: npt.DTypeLike, copy: bool = ...) -> np.ndarray:
+        ...
+
+    @overload
+    def astype(self, dtype: ExtensionDtype, copy: bool = ...) -> ExtensionArray:
+        ...
+
+    @overload
+    def astype(self, dtype: AstypeArg, copy: bool = ...) -> ArrayLike:
+        ...
+
+    def astype(self, dtype: AstypeArg, copy: bool = True) -> ArrayLike:
         """
         Cast to a NumPy array or ExtensionArray with 'dtype'.
 
diff --git a/pandas/core/arrays/integer.py b/pandas/core/arrays/integer.py
index c9ba762a271bd..e62a2f95b0340 100644
--- a/pandas/core/arrays/integer.py
+++ b/pandas/core/arrays/integer.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+from typing import overload
 import warnings
 
 import numpy as np
@@ -11,8 +12,10 @@
 )
 from pandas._typing import (
     ArrayLike,
+    AstypeArg,
     Dtype,
     DtypeObj,
+    npt,
 )
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import cache_readonly
@@ -33,6 +36,7 @@
 )
 from pandas.core.dtypes.missing import isna
 
+from pandas.core.arrays import ExtensionArray
 from pandas.core.arrays.masked import (
     BaseMaskedArray,
     BaseMaskedDtype,
@@ -333,7 +337,19 @@ def _from_sequence_of_strings(
     def _coerce_to_array(self, value) -> tuple[np.ndarray, np.ndarray]:
         return coerce_to_array(value, dtype=self.dtype)
 
-    def astype(self, dtype, copy: bool = True) -> ArrayLike:
+    @overload
+    def astype(self, dtype: npt.DTypeLike, copy: bool = ...) -> np.ndarray:
+        ...
+
+    @overload
+    def astype(self, dtype: ExtensionDtype, copy: bool = ...) -> ExtensionArray:
+        ...
+
+    @overload
+    def astype(self, dtype: AstypeArg, copy: bool = ...) -> ArrayLike:
+        ...
+
+    def astype(self, dtype: AstypeArg, copy: bool = True) -> ArrayLike:
         """
         Cast to a NumPy array or ExtensionArray with 'dtype'.
 
diff --git a/pandas/core/arrays/masked.py b/pandas/core/arrays/masked.py
index 718e135464385..cccfd58aa914d 100644
--- a/pandas/core/arrays/masked.py
+++ b/pandas/core/arrays/masked.py
@@ -5,6 +5,7 @@
     Any,
     Sequence,
     TypeVar,
+    overload,
 )
 
 import numpy as np
@@ -15,10 +16,11 @@
 )
 from pandas._typing import (
     ArrayLike,
-    Dtype,
+    AstypeArg,
     NpDtype,
     PositionalIndexer,
     Scalar,
+    npt,
     type_t,
 )
 from pandas.errors import AbstractMethodError
@@ -282,9 +284,7 @@ def to_numpy(  # type: ignore[override]
         if na_value is lib.no_default:
             na_value = libmissing.NA
         if dtype is None:
-            # error: Incompatible types in assignment (expression has type
-            # "Type[object]", variable has type "Union[str, dtype[Any], None]")
-            dtype = object  # type: ignore[assignment]
+            dtype = object
         if self._hasna:
             if (
                 not is_object_dtype(dtype)
@@ -303,7 +303,19 @@ def to_numpy(  # type: ignore[override]
             data = self._data.astype(dtype, copy=copy)
         return data
 
-    def astype(self, dtype: Dtype, copy: bool = True) -> ArrayLike:
+    @overload
+    def astype(self, dtype: npt.DTypeLike, copy: bool = ...) -> np.ndarray:
+        ...
+
+    @overload
+    def astype(self, dtype: ExtensionDtype, copy: bool = ...) -> ExtensionArray:
+        ...
+
+    @overload
+    def astype(self, dtype: AstypeArg, copy: bool = ...) -> ArrayLike:
+        ...
+
+    def astype(self, dtype: AstypeArg, copy: bool = True) -> ArrayLike:
         dtype = pandas_dtype(dtype)
 
         if is_dtype_equal(dtype, self.dtype):
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index 488981bcc9687..2db1f00e237ee 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -351,9 +351,7 @@ def freq(self) -> BaseOffset:
     def __array__(self, dtype: NpDtype | None = None) -> np.ndarray:
         if dtype == "i8":
             return self.asi8
-        # error: Non-overlapping equality check (left operand type: "Optional[Union[str,
-        # dtype[Any]]]", right operand type: "Type[bool]")
-        elif dtype == bool:  # type: ignore[comparison-overlap]
+        elif dtype == bool:
             return ~self._isnan
 
         # This will raise TypeError for non-object dtypes
diff --git a/pandas/core/arrays/sparse/array.py b/pandas/core/arrays/sparse/array.py
index b1c794ac03b31..6dce9b4475d1b 100644
--- a/pandas/core/arrays/sparse/array.py
+++ b/pandas/core/arrays/sparse/array.py
@@ -27,6 +27,7 @@
 from pandas._libs.tslibs import NaT
 from pandas._typing import (
     ArrayLike,
+    AstypeArg,
     Dtype,
     NpDtype,
     Scalar,
@@ -527,9 +528,7 @@ def __array__(self, dtype: NpDtype | None = None) -> np.ndarray:
             try:
                 dtype = np.result_type(self.sp_values.dtype, type(fill_value))
             except TypeError:
-                # error: Incompatible types in assignment (expression has type
-                # "Type[object]", variable has type "Union[str, dtype[Any], None]")
-                dtype = object  # type: ignore[assignment]
+                dtype = object
 
         out = np.full(self.shape, fill_value, dtype=dtype)
         out[self.sp_index.to_int_index().indices] = self.sp_values
@@ -1072,7 +1071,7 @@ def _concat_same_type(
 
         return cls(data, sparse_index=sp_index, fill_value=fill_value)
 
-    def astype(self, dtype: Dtype | None = None, copy=True):
+    def astype(self, dtype: AstypeArg | None = None, copy=True):
         """
         Change the dtype of a SparseArray.
 
diff --git a/pandas/core/common.py b/pandas/core/common.py
index b32614577393d..2bf925466e176 100644
--- a/pandas/core/common.py
+++ b/pandas/core/common.py
@@ -232,12 +232,7 @@ def asarray_tuplesafe(values, dtype: NpDtype | None = None) -> np.ndarray:
         # expected "ndarray")
         return values._values  # type: ignore[return-value]
 
-    # error: Non-overlapping container check (element type: "Union[str, dtype[Any],
-    # None]", container item type: "type")
-    if isinstance(values, list) and dtype in [  # type: ignore[comparison-overlap]
-        np.object_,
-        object,
-    ]:
+    if isinstance(values, list) and dtype in [np.object_, object]:
         return construct_1d_object_array_from_listlike(values)
 
     result = np.asarray(values, dtype=dtype)
diff --git a/pandas/core/dtypes/dtypes.py b/pandas/core/dtypes/dtypes.py
index bf1f5d37f07dc..6be2e803b5910 100644
--- a/pandas/core/dtypes/dtypes.py
+++ b/pandas/core/dtypes/dtypes.py
@@ -29,8 +29,8 @@
 from pandas._typing import (
     Dtype,
     DtypeObj,
-    NpDtype,
     Ordered,
+    npt,
     type_t,
 )
 
@@ -1294,7 +1294,7 @@ class PandasDtype(ExtensionDtype):
 
     _metadata = ("_dtype",)
 
-    def __init__(self, dtype: NpDtype | PandasDtype | None):
+    def __init__(self, dtype: npt.DTypeLike | PandasDtype | None):
         if isinstance(dtype, PandasDtype):
             # make constructor univalent
             dtype = dtype.numpy_dtype
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index 0010624609907..e3fcff1557ca9 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1369,7 +1369,7 @@ def get_values(self, dtype: DtypeObj | None = None) -> np.ndarray:
         """
         return object dtype as boxed values, such as Timestamps/Timedelta
         """
-        values = self.values
+        values: ArrayLike = self.values
         if dtype == _dtype_obj:
             values = values.astype(object)
         # TODO(EA2D): reshape not needed with 2D EAs