diff --git a/pandas/tests/extension/base/__init__.py b/pandas/tests/extension/base/__init__.py
index 0e9a35b9f07e8..7d76838998540 100644
--- a/pandas/tests/extension/base/__init__.py
+++ b/pandas/tests/extension/base/__init__.py
@@ -60,6 +60,7 @@ class TestMyDtype(BaseDtypeTests):
     BaseBooleanReduceTests,
     BaseNoReduceTests,
     BaseNumericReduceTests,
+    BaseReduceTests,
 )
 from pandas.tests.extension.base.reshaping import BaseReshapingTests  # noqa: F401
 from pandas.tests.extension.base.setitem import BaseSetitemTests  # noqa: F401
diff --git a/pandas/tests/extension/base/reduce.py b/pandas/tests/extension/base/reduce.py
index b7edfb860549c..00919b16a2600 100644
--- a/pandas/tests/extension/base/reduce.py
+++ b/pandas/tests/extension/base/reduce.py
@@ -15,6 +15,10 @@ class BaseReduceTests(BaseExtensionTests):
     make sense for numeric/boolean operations.
     """
 
+    def _supports_reduction(self, obj, op_name: str) -> bool:
+        # Specify if we expect this reduction to succeed.
+        return False
+
     def check_reduce(self, s, op_name, skipna):
         # We perform the same operation on the np.float64 data and check
         #  that the results match. Override if you need to cast to something
@@ -66,47 +70,42 @@ def check_reduce_frame(self, ser: pd.Series, op_name: str, skipna: bool):
 
         tm.assert_extension_array_equal(result1, expected)
 
-
-class BaseNoReduceTests(BaseReduceTests):
-    """we don't define any reductions"""
-
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_reduce_series_numeric(self, data, all_numeric_reductions, skipna):
-        op_name = all_numeric_reductions
-        s = pd.Series(data)
-
-        msg = (
-            "[Cc]annot perform|Categorical is not ordered for operation|"
-            "does not support reduction|"
-        )
-
-        with pytest.raises(TypeError, match=msg):
-            getattr(s, op_name)(skipna=skipna)
-
     @pytest.mark.parametrize("skipna", [True, False])
     def test_reduce_series_boolean(self, data, all_boolean_reductions, skipna):
         op_name = all_boolean_reductions
         s = pd.Series(data)
 
-        msg = (
-            "[Cc]annot perform|Categorical is not ordered for operation|"
-            "does not support reduction|"
-        )
+        if not self._supports_reduction(s, op_name):
+            msg = (
+                "[Cc]annot perform|Categorical is not ordered for operation|"
+                "does not support reduction|"
+            )
 
-        with pytest.raises(TypeError, match=msg):
-            getattr(s, op_name)(skipna=skipna)
+            with pytest.raises(TypeError, match=msg):
+                getattr(s, op_name)(skipna=skipna)
 
+        else:
+            self.check_reduce(s, op_name, skipna)
 
-class BaseNumericReduceTests(BaseReduceTests):
     @pytest.mark.parametrize("skipna", [True, False])
-    def test_reduce_series(self, data, all_numeric_reductions, skipna):
+    def test_reduce_series_numeric(self, data, all_numeric_reductions, skipna):
         op_name = all_numeric_reductions
         s = pd.Series(data)
 
-        # min/max with empty produce numpy warnings
-        with warnings.catch_warnings():
-            warnings.simplefilter("ignore", RuntimeWarning)
-            self.check_reduce(s, op_name, skipna)
+        if not self._supports_reduction(s, op_name):
+            msg = (
+                "[Cc]annot perform|Categorical is not ordered for operation|"
+                "does not support reduction|"
+            )
+
+            with pytest.raises(TypeError, match=msg):
+                getattr(s, op_name)(skipna=skipna)
+
+        else:
+            # min/max with empty produce numpy warnings
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", RuntimeWarning)
+                self.check_reduce(s, op_name, skipna)
 
     @pytest.mark.parametrize("skipna", [True, False])
     def test_reduce_frame(self, data, all_numeric_reductions, skipna):
@@ -118,12 +117,28 @@ def test_reduce_frame(self, data, all_numeric_reductions, skipna):
         if op_name in ["count", "kurt", "sem"]:
             pytest.skip(f"{op_name} not an array method")
 
+        if not self._supports_reduction(s, op_name):
+            pytest.skip(f"Reduction {op_name} not supported for this dtype")
+
         self.check_reduce_frame(s, op_name, skipna)
 
 
+# TODO: deprecate BaseNoReduceTests, BaseNumericReduceTests, BaseBooleanReduceTests
+class BaseNoReduceTests(BaseReduceTests):
+    """we don't define any reductions"""
+
+
+class BaseNumericReduceTests(BaseReduceTests):
+    # For backward compatibility only, this only runs the numeric reductions
+    def _supports_reduction(self, obj, op_name: str) -> bool:
+        if op_name in ["any", "all"]:
+            pytest.skip("These are tested in BaseBooleanReduceTests")
+        return True
+
+
 class BaseBooleanReduceTests(BaseReduceTests):
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_reduce_series(self, data, all_boolean_reductions, skipna):
-        op_name = all_boolean_reductions
-        s = pd.Series(data)
-        self.check_reduce(s, op_name, skipna)
+    # For backward compatibility only, this only runs the numeric reductions
+    def _supports_reduction(self, obj, op_name: str) -> bool:
+        if op_name not in ["any", "all"]:
+            pytest.skip("These are tested in BaseNumericReduceTests")
+        return True
diff --git a/pandas/tests/extension/decimal/test_decimal.py b/pandas/tests/extension/decimal/test_decimal.py
index 944ed0dbff66e..b2dd910fd0d2d 100644
--- a/pandas/tests/extension/decimal/test_decimal.py
+++ b/pandas/tests/extension/decimal/test_decimal.py
@@ -146,6 +146,9 @@ def test_fillna_series_method(self, data_missing, fillna_method):
 
 
 class Reduce:
+    def _supports_reduction(self, obj, op_name: str) -> bool:
+        return True
+
     def check_reduce(self, s, op_name, skipna):
         if op_name in ["median", "skew", "kurt", "sem"]:
             msg = r"decimal does not support the .* operation"
@@ -183,7 +186,7 @@ def _reduce(self, name: str, *, skipna: bool = True, **kwargs):
         tm.assert_series_equal(result, expected)
 
 
-class TestNumericReduce(Reduce, base.BaseNumericReduceTests):
+class TestReduce(Reduce, base.BaseReduceTests):
     @pytest.mark.parametrize("skipna", [True, False])
     def test_reduce_frame(self, data, all_numeric_reductions, skipna):
         op_name = all_numeric_reductions
@@ -194,10 +197,6 @@ def test_reduce_frame(self, data, all_numeric_reductions, skipna):
         return super().test_reduce_frame(data, all_numeric_reductions, skipna)
 
 
-class TestBooleanReduce(Reduce, base.BaseBooleanReduceTests):
-    pass
-
-
 class TestMethods(base.BaseMethodsTests):
     def test_fillna_copy_frame(self, data_missing, using_copy_on_write):
         warn = FutureWarning if not using_copy_on_write else None
diff --git a/pandas/tests/extension/json/test_json.py b/pandas/tests/extension/json/test_json.py
index 8a571d9295e1f..fa3314e36c974 100644
--- a/pandas/tests/extension/json/test_json.py
+++ b/pandas/tests/extension/json/test_json.py
@@ -175,7 +175,7 @@ def test_fillna_frame(self):
 unhashable = pytest.mark.xfail(reason="Unhashable")
 
 
-class TestReduce(base.BaseNoReduceTests):
+class TestReduce(base.BaseReduceTests):
     pass
 
 
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 655ca9cc39c58..eae97fceab2f7 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -408,7 +408,10 @@ def test_accumulate_series(self, data, all_numeric_accumulations, skipna, reques
         self.check_accumulate(ser, op_name, skipna)
 
 
-class TestBaseNumericReduce(base.BaseNumericReduceTests):
+class TestReduce(base.BaseReduceTests):
+    def _supports_reduction(self, obj, op_name: str) -> bool:
+        return True
+
     def check_reduce(self, ser, op_name, skipna):
         pa_dtype = ser.dtype.pyarrow_dtype
         if op_name == "count":
@@ -429,7 +432,7 @@ def check_reduce(self, ser, op_name, skipna):
         tm.assert_almost_equal(result, expected)
 
     @pytest.mark.parametrize("skipna", [True, False])
-    def test_reduce_series(self, data, all_numeric_reductions, skipna, request):
+    def test_reduce_series_numeric(self, data, all_numeric_reductions, skipna, request):
         pa_dtype = data.dtype.pyarrow_dtype
         opname = all_numeric_reductions
 
@@ -497,44 +500,10 @@ def test_reduce_series(self, data, all_numeric_reductions, skipna, request):
             "median",
         }:
             request.node.add_marker(xfail_mark)
-        super().test_reduce_series(data, all_numeric_reductions, skipna)
-
-    def _get_expected_reduction_dtype(self, arr, op_name: str):
-        if op_name in ["max", "min"]:
-            cmp_dtype = arr.dtype
-        elif arr.dtype.name == "decimal128(7, 3)[pyarrow]":
-            if op_name not in ["median", "var", "std"]:
-                cmp_dtype = arr.dtype
-            else:
-                cmp_dtype = "float64[pyarrow]"
-        elif op_name in ["median", "var", "std", "mean", "skew"]:
-            cmp_dtype = "float64[pyarrow]"
-        else:
-            cmp_dtype = {
-                "i": "int64[pyarrow]",
-                "u": "uint64[pyarrow]",
-                "f": "float64[pyarrow]",
-            }[arr.dtype.kind]
-        return cmp_dtype
+        super().test_reduce_series_numeric(data, all_numeric_reductions, skipna)
 
     @pytest.mark.parametrize("skipna", [True, False])
-    def test_reduce_frame(self, data, all_numeric_reductions, skipna):
-        op_name = all_numeric_reductions
-        if op_name == "skew":
-            assert not hasattr(data, op_name)
-            return
-        return super().test_reduce_frame(data, all_numeric_reductions, skipna)
-
-    @pytest.mark.parametrize("typ", ["int64", "uint64", "float64"])
-    def test_median_not_approximate(self, typ):
-        # GH 52679
-        result = pd.Series([1, 2], dtype=f"{typ}[pyarrow]").median()
-        assert result == 1.5
-
-
-class TestBaseBooleanReduce(base.BaseBooleanReduceTests):
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_reduce_series(
+    def test_reduce_series_boolean(
         self, data, all_boolean_reductions, skipna, na_value, request
     ):
         pa_dtype = data.dtype.pyarrow_dtype
@@ -566,6 +535,38 @@ def test_reduce_series(
         result = getattr(ser, op_name)(skipna=skipna)
         assert result is (op_name == "any")
 
+    def _get_expected_reduction_dtype(self, arr, op_name: str):
+        if op_name in ["max", "min"]:
+            cmp_dtype = arr.dtype
+        elif arr.dtype.name == "decimal128(7, 3)[pyarrow]":
+            if op_name not in ["median", "var", "std"]:
+                cmp_dtype = arr.dtype
+            else:
+                cmp_dtype = "float64[pyarrow]"
+        elif op_name in ["median", "var", "std", "mean", "skew"]:
+            cmp_dtype = "float64[pyarrow]"
+        else:
+            cmp_dtype = {
+                "i": "int64[pyarrow]",
+                "u": "uint64[pyarrow]",
+                "f": "float64[pyarrow]",
+            }[arr.dtype.kind]
+        return cmp_dtype
+
+    @pytest.mark.parametrize("skipna", [True, False])
+    def test_reduce_frame(self, data, all_numeric_reductions, skipna):
+        op_name = all_numeric_reductions
+        if op_name == "skew":
+            assert not hasattr(data, op_name)
+            return
+        return super().test_reduce_frame(data, all_numeric_reductions, skipna)
+
+    @pytest.mark.parametrize("typ", ["int64", "uint64", "float64"])
+    def test_median_not_approximate(self, typ):
+        # GH 52679
+        result = pd.Series([1, 2], dtype=f"{typ}[pyarrow]").median()
+        assert result == 1.5
+
 
 class TestBaseGroupby(base.BaseGroupbyTests):
     def test_in_numeric_groupby(self, data_for_grouping):
diff --git a/pandas/tests/extension/test_boolean.py b/pandas/tests/extension/test_boolean.py
index e5f6da5371742..229f1f4ec028c 100644
--- a/pandas/tests/extension/test_boolean.py
+++ b/pandas/tests/extension/test_boolean.py
@@ -220,7 +220,10 @@ def test_groupby_sum_mincount(self, data_for_grouping, min_count):
             tm.assert_frame_equal(result, expected)
 
 
-class TestNumericReduce(base.BaseNumericReduceTests):
+class TestReduce(base.BaseReduceTests):
+    def _supports_reduction(self, obj, op_name: str) -> bool:
+        return True
+
     def check_reduce(self, s, op_name, skipna):
         if op_name == "count":
             result = getattr(s, op_name)()
@@ -248,10 +251,6 @@ def _get_expected_reduction_dtype(self, arr, op_name: str):
         return cmp_dtype
 
 
-class TestBooleanReduce(base.BaseBooleanReduceTests):
-    pass
-
-
 class TestPrinting(base.BasePrintingTests):
     pass
 
diff --git a/pandas/tests/extension/test_categorical.py b/pandas/tests/extension/test_categorical.py
index fc4dfe3af3bca..e24d29ea53908 100644
--- a/pandas/tests/extension/test_categorical.py
+++ b/pandas/tests/extension/test_categorical.py
@@ -152,7 +152,7 @@ class TestMissing(base.BaseMissingTests):
     pass
 
 
-class TestReduce(base.BaseNoReduceTests):
+class TestReduce(base.BaseReduceTests):
     pass
 
 
diff --git a/pandas/tests/extension/test_interval.py b/pandas/tests/extension/test_interval.py
index 4ef303289ee5c..b4870d2f1fe2f 100644
--- a/pandas/tests/extension/test_interval.py
+++ b/pandas/tests/extension/test_interval.py
@@ -105,7 +105,7 @@ class TestInterface(BaseInterval, base.BaseInterfaceTests):
     pass
 
 
-class TestReduce(base.BaseNoReduceTests):
+class TestReduce(base.BaseReduceTests):
     @pytest.mark.parametrize("skipna", [True, False])
     def test_reduce_series_numeric(self, data, all_numeric_reductions, skipna):
         op_name = all_numeric_reductions
diff --git a/pandas/tests/extension/test_masked_numeric.py b/pandas/tests/extension/test_masked_numeric.py
index b171797dd6359..cb3792d37831d 100644
--- a/pandas/tests/extension/test_masked_numeric.py
+++ b/pandas/tests/extension/test_masked_numeric.py
@@ -227,7 +227,12 @@ class TestGroupby(base.BaseGroupbyTests):
     pass
 
 
-class TestNumericReduce(base.BaseNumericReduceTests):
+class TestReduce(base.BaseReduceTests):
+    def _supports_reduction(self, obj, op_name: str) -> bool:
+        if op_name in ["any", "all"]:
+            pytest.skip(reason="Tested in tests/reductions/test_reductions.py")
+        return True
+
     def check_reduce(self, ser: pd.Series, op_name: str, skipna: bool):
         # overwrite to ensure pd.NA is tested instead of np.nan
         # https://github.com/pandas-dev/pandas/issues/30958
@@ -266,11 +271,6 @@ def _get_expected_reduction_dtype(self, arr, op_name: str):
         return cmp_dtype
 
 
-@pytest.mark.skip(reason="Tested in tests/reductions/test_reductions.py")
-class TestBooleanReduce(base.BaseBooleanReduceTests):
-    pass
-
-
 class TestAccumulation(base.BaseAccumulateTests):
     def _supports_accumulation(self, ser: pd.Series, op_name: str) -> bool:
         return True
diff --git a/pandas/tests/extension/test_numpy.py b/pandas/tests/extension/test_numpy.py
index db191954c8d59..14f98e4115e4e 100644
--- a/pandas/tests/extension/test_numpy.py
+++ b/pandas/tests/extension/test_numpy.py
@@ -303,11 +303,22 @@ class TestPrinting(BaseNumPyTests, base.BasePrintingTests):
     pass
 
 
-class TestNumericReduce(BaseNumPyTests, base.BaseNumericReduceTests):
+class TestReduce(BaseNumPyTests, base.BaseReduceTests):
+    def _supports_reduction(self, obj, op_name: str) -> bool:
+        if tm.get_dtype(obj).kind == "O":
+            return op_name in ["sum", "min", "max", "any", "all"]
+        return True
+
     def check_reduce(self, s, op_name, skipna):
-        result = getattr(s, op_name)(skipna=skipna)
+        res_op = getattr(s, op_name)
         # avoid coercing int -> float. Just cast to the actual numpy type.
-        expected = getattr(s.astype(s.dtype._dtype), op_name)(skipna=skipna)
+        exp_op = getattr(s.astype(s.dtype._dtype), op_name)
+        if op_name == "count":
+            result = res_op()
+            expected = exp_op()
+        else:
+            result = res_op(skipna=skipna)
+            expected = exp_op(skipna=skipna)
         tm.assert_almost_equal(result, expected)
 
     @pytest.mark.skip("tests not written yet")
@@ -315,15 +326,6 @@ def check_reduce(self, s, op_name, skipna):
     def test_reduce_frame(self, data, all_numeric_reductions, skipna):
         pass
 
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_reduce_series(self, data, all_boolean_reductions, skipna):
-        super().test_reduce_series(data, all_boolean_reductions, skipna)
-
-
-@skip_nested
-class TestBooleanReduce(BaseNumPyTests, base.BaseBooleanReduceTests):
-    pass
-
 
 class TestMissing(BaseNumPyTests, base.BaseMissingTests):
     @skip_nested
diff --git a/pandas/tests/extension/test_string.py b/pandas/tests/extension/test_string.py
index d42d79da17f4e..7256ea5837bbf 100644
--- a/pandas/tests/extension/test_string.py
+++ b/pandas/tests/extension/test_string.py
@@ -168,7 +168,7 @@ def test_fillna_no_op_returns_copy(self, data):
         tm.assert_extension_array_equal(result, data)
 
 
-class TestNoReduce(base.BaseNoReduceTests):
+class TestReduce(base.BaseReduceTests):
     @pytest.mark.parametrize("skipna", [True, False])
     def test_reduce_series_numeric(self, data, all_numeric_reductions, skipna):
         op_name = all_numeric_reductions