diff --git a/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/lagrange_first.csv b/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/lagrange_first.csv
new file mode 100644
index 000000000000..af4161fd00b7
--- /dev/null
+++ b/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/lagrange_first.csv
@@ -0,0 +1,5 @@
+time,average_diff
+1,0.2020775739487
+2,0.46723439754399
+3,0.70930261331699
+4,0.95137082908996
diff --git a/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/monomial_constant.csv b/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/monomial_constant.csv
new file mode 100644
index 000000000000..2bb03dde5e3f
--- /dev/null
+++ b/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/monomial_constant.csv
@@ -0,0 +1,5 @@
+time,average_diff
+1,0.75617392941647
+2,1.8889059704735
+3,2.9855536197061
+4,4.1002434648509
diff --git a/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/monomial_first.csv b/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/monomial_first.csv
new file mode 100644
index 000000000000..6d6e202a030f
--- /dev/null
+++ b/modules/tensor_mechanics/test/tests/projected_stateful_materials/gold/monomial_first.csv
@@ -0,0 +1,5 @@
+time,average_diff
+1,1.1012393020396e-14
+2,8.8494811211044e-15
+3,1.5159757740515e-14
+4,2.6153760064151e-14
diff --git a/modules/tensor_mechanics/test/tests/projected_stateful_materials/test.i b/modules/tensor_mechanics/test/tests/projected_stateful_materials/test.i
index 8ad5d183e039..c548aa7f04ad 100644
--- a/modules/tensor_mechanics/test/tests/projected_stateful_materials/test.i
+++ b/modules/tensor_mechanics/test/tests/projected_stateful_materials/test.i
@@ -42,7 +42,7 @@
 
 [Executioner]
   type = Transient
-  num_steps = 3
+  num_steps = 4
 []
 
 [Outputs]
diff --git a/modules/tensor_mechanics/test/tests/projected_stateful_materials/tests b/modules/tensor_mechanics/test/tests/projected_stateful_materials/tests
index e69de29bb2d1..45e13d177420 100644
--- a/modules/tensor_mechanics/test/tests/projected_stateful_materials/tests
+++ b/modules/tensor_mechanics/test/tests/projected_stateful_materials/tests
@@ -0,0 +1,32 @@
+[Tests]
+  issues = '#26053'
+  design = 'ProjectedStatefulMaterialStorageAction.md'
+
+  [monomial_first]
+    type = CSVDiff
+    input = test.i
+    cli_args = 'Outputs/file_base=monomial_first'
+    csvdiff = monomial_first.csv
+    allow_test_objects = true
+    requirement = "The system shall support the storage of old material property states projected "
+                  "onto a first order monomial basis."
+  []
+  [monomial_constant]
+    type = CSVDiff
+    input = test.i
+    cli_args = 'Outputs/file_base=monomial_constant ProjectedStatefulMaterialStorage/all/order=CONSTANT'
+    csvdiff = monomial_constant.csv
+    allow_test_objects = true
+    requirement = "The system shall support the storage of old material property states projected "
+                  "onto a constant monomial basis."
+  []
+  [lagrange_first]
+    type = CSVDiff
+    input = test.i
+    cli_args = 'Outputs/file_base=lagrange_first ProjectedStatefulMaterialStorage/all/family=LAGRANGE'
+    csvdiff = lagrange_first.csv
+    allow_test_objects = true
+    requirement = "The system shall support the storage of old material property states projected "
+                  "onto a first order lagrange basis."
+  []
+[]