diff --git a/pandas/tests/extension/test_string.py b/pandas/tests/extension/test_string.py
index e1f2db149edf9..17f6eb8282b23 100644
--- a/pandas/tests/extension/test_string.py
+++ b/pandas/tests/extension/test_string.py
@@ -22,7 +22,7 @@
 import numpy as np
 import pytest
 
-from pandas._config import using_string_dtype
+from pandas.compat import HAS_PYARROW
 
 import pandas as pd
 import pandas._testing as tm
@@ -31,10 +31,6 @@
 from pandas.core.arrays.string_ import StringDtype
 from pandas.tests.extension import base
 
-pytestmark = pytest.mark.xfail(
-    using_string_dtype(), reason="TODO(infer_string)", strict=False
-)
-
 
 def maybe_split_array(arr, chunked):
     if not chunked:
@@ -217,6 +213,36 @@ def test_compare_scalar(self, data, comparison_op):
     def test_groupby_extension_apply(self, data_for_grouping, groupby_apply_op):
         super().test_groupby_extension_apply(data_for_grouping, groupby_apply_op)
 
+    def test_combine_add(self, data_repeated, using_infer_string, request):
+        dtype = next(data_repeated(1)).dtype
+        if using_infer_string and (
+            (dtype.na_value is pd.NA) and dtype.storage == "python"
+        ):
+            mark = pytest.mark.xfail(
+                reason="The pointwise operation result will be inferred to "
+                "string[nan, pyarrow], which does not match the input dtype"
+            )
+            request.applymarker(mark)
+        super().test_combine_add(data_repeated)
+
+    def test_arith_series_with_array(
+        self, data, all_arithmetic_operators, using_infer_string, request
+    ):
+        dtype = data.dtype
+        if (
+            using_infer_string
+            and all_arithmetic_operators == "__radd__"
+            and (
+                (dtype.na_value is pd.NA) or (dtype.storage == "python" and HAS_PYARROW)
+            )
+        ):
+            mark = pytest.mark.xfail(
+                reason="The pointwise operation result will be inferred to "
+                "string[nan, pyarrow], which does not match the input dtype"
+            )
+            request.applymarker(mark)
+        super().test_arith_series_with_array(data, all_arithmetic_operators)
+
 
 class Test2DCompat(base.Dim2CompatTests):
     @pytest.fixture(autouse=True)