diff --git a/tensorflow/python/distribute/values_test.py b/tensorflow/python/distribute/values_test.py
index 447a8b427eb..a9d7dd2125e 100644
--- a/tensorflow/python/distribute/values_test.py
+++ b/tensorflow/python/distribute/values_test.py
@@ -26,6 +26,7 @@ import numpy as np
 
 from tensorflow.core.protobuf import config_pb2
 from tensorflow.python import tf2
+from tensorflow.python.distribute import collective_all_reduce_strategy
 from tensorflow.python.distribute import combinations
 from tensorflow.python.distribute import distribute_lib
 from tensorflow.python.distribute import distribute_utils
@@ -408,6 +409,9 @@ class DistributedDelegateTest(test.TestCase):
             strategy_combinations.tpu_strategy,
             strategy_combinations.tpu_strategy_packed_var,
             strategy_combinations.central_storage_strategy_with_two_gpus,
+            strategy_combinations.multi_worker_mirrored_2x1_cpu,
+            strategy_combinations.multi_worker_mirrored_2x1_gpu,
+            strategy_combinations.multi_worker_mirrored_2x2_gpu
         ],
         synchronization=[
             variables_lib.VariableSynchronization.ON_READ,
@@ -427,7 +431,19 @@ class DistributedVariableTest(test.TestCase, parameterized.TestCase):
           1., synchronization=synchronization, aggregation=aggregation)
     self.assertIsInstance(v, variables_lib.Variable)
 
-  def testCheckpointing(self, distribution, synchronization, aggregation):
+  def testCheckpointing(self, distribution, synchronization, aggregation, mode):
+    # TODO(anjs): Remove this when b/162147051 is fixed.
+    if (isinstance(distribution,
+                   collective_all_reduce_strategy.CollectiveAllReduceStrategy)
+        and aggregation == variables_lib.VariableAggregation.SUM
+        and synchronization == variables_lib.VariableSynchronization.ON_READ):
+      self.skipTest("b/162147051")
+
+    if (isinstance(distribution,
+                   collective_all_reduce_strategy.CollectiveAllReduceStrategy)
+        and mode == "graph"):
+      self.skipTest("MWMS combinations tests do not work well in graph mode.")
+
     with distribution.scope():
       v = variables_lib.Variable(
           constant_op.constant([1., 2., 3., 4]),
@@ -594,6 +610,12 @@ class DistributedVariableTest(test.TestCase, parameterized.TestCase):
       self.skipTest("b/148689177: AggregatingVariable doesn't "
                     "conform to Variable interface well")
 
+    # TODO(crccw): Unskip this in cl/323875091.
+    if (isinstance(
+        distribution,
+        collective_all_reduce_strategy.CollectiveAllReduceStrategy)):
+      self.skipTest("Being fixed in cl/323875091")
+
     # tf.function requires the return value to be Tensors, which is not always
     # case for properties and methods of Variable, so we simply discard the
     # return values.