diff --git a/pandas/tests/arrays/test_datetimelike.py b/pandas/tests/arrays/test_datetimelike.py
index 7f85c891afeed..4961123a7ca07 100644
--- a/pandas/tests/arrays/test_datetimelike.py
+++ b/pandas/tests/arrays/test_datetimelike.py
@@ -659,7 +659,9 @@ def test_array_interface(self, datetime_index):
         assert result is expected
         tm.assert_numpy_array_equal(result, expected)
         result = np.array(arr, dtype="datetime64[ns]")
-        assert result is not expected
+        if not np_version_gt2:
+            # TODO: GH 57739
+            assert result is not expected
         tm.assert_numpy_array_equal(result, expected)
 
         # to object dtype
@@ -974,7 +976,9 @@ def test_array_interface(self, timedelta_index):
         assert result is expected
         tm.assert_numpy_array_equal(result, expected)
         result = np.array(arr, dtype="timedelta64[ns]")
-        assert result is not expected
+        if not np_version_gt2:
+            # TODO: GH 57739
+            assert result is not expected
         tm.assert_numpy_array_equal(result, expected)
 
         # to object dtype
diff --git a/pandas/tests/extension/base/missing.py b/pandas/tests/extension/base/missing.py
index dbd6682c12123..fb15b2dec869c 100644
--- a/pandas/tests/extension/base/missing.py
+++ b/pandas/tests/extension/base/missing.py
@@ -27,7 +27,9 @@ def test_isna_returns_copy(self, data_missing, na_func):
         expected = result.copy()
         mask = getattr(result, na_func)()
         if isinstance(mask.dtype, pd.SparseDtype):
+            # TODO: GH 57739
             mask = np.array(mask)
+            mask.flags.writeable = True
 
         mask[:] = True
         tm.assert_series_equal(result, expected)
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index b7204d7af1cbb..7eeb626d91dc8 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -71,8 +71,8 @@ def test_constructor_casting(self, index):
         tm.assert_contains_all(arr, new_index)
         tm.assert_index_equal(index, new_index)
 
-    @pytest.mark.parametrize("index", ["string"], indirect=True)
-    def test_constructor_copy(self, index, using_infer_string):
+    def test_constructor_copy(self, using_infer_string):
+        index = Index(list("abc"), name="name")
         arr = np.array(index)
         new_index = Index(arr, copy=True, name="name")
         assert isinstance(new_index, Index)