diff --git a/tests/test_model_composition.py b/tests/test_model_composition.py
index 68024f5a..8f0e00e2 100644
--- a/tests/test_model_composition.py
+++ b/tests/test_model_composition.py
@@ -63,6 +63,62 @@
     ]
 )
 
+S1 = Concept(name="Susceptible", identifiers={"ido": "0000514"})
+I1 = Concept(name="Infected", identifiers={"ido": "0000511"})
+R1 = Concept(name="Recovery", identifiers={"ido": "0000592"})
+
+S2 = Concept(name="Susceptible", identifiers={"ido": "0000513"})
+I2 = Concept(name="Infected", identifiers={"ido": "0000512"})
+R2 = Concept(name="Recovery", identifiers={"ido": "0000593"})
+
+S3 = Concept(name="S", identifiers={"ido": "0000514"})
+I3 = Concept(name="I", identifiers={"ido": "0000511"})
+R3 = Concept(name="R", identifiers={"ido": "0000592"})
+
+S4 = Concept(name="S")
+I4 = Concept(name="I")
+R4 = Concept(name="R")
+
+model_A1 = TemplateModel(
+    templates=[
+        ControlledConversion(
+            name="Infection", subject=S1, outcome=I1, controller=I1
+        )
+    ]
+)
+
+model_B1 = TemplateModel(
+    templates=[NaturalConversion(name="Recovery", subject=I1, outcome=R1)]
+)
+
+model_B2 = TemplateModel(
+    templates=[NaturalConversion(name="Recovery", subject=I2, outcome=R2)]
+)
+
+model_B3 = TemplateModel(
+    templates=[NaturalConversion(name="Recovery", subject=I3, outcome=R3)]
+)
+
+model_B4 = TemplateModel(
+    templates=[NaturalConversion(name="Recovery", subject=I4, outcome=R4)]
+)
+
+model_A3 = TemplateModel(
+    templates=[
+        ControlledConversion(
+            name="Infection", subject=S3, outcome=I3, controller=I3
+        )
+    ]
+)
+
+model_A4 = TemplateModel(
+    templates=[
+        ControlledConversion(
+            name="Infection", subject=S4, outcome=I4, controller=I4
+        )
+    ]
+)
+
 
 def test_compose_two_models():
     composed_model = compose_two_models(sir_reinfection, sir)
@@ -116,3 +172,70 @@ def test_template_inclusion():
     composed template model"""
     composed_tm = compose_two_models(mini_sir, sir)
     assert len(composed_tm.templates) == 2
+
+
+def test_concept_composition():
+    """We test model composition's consolidation of concepts using test-cases
+    described in this issue here: https://github.com/gyorilab/mira/issues/409
+    """
+    model_ab11 = compose([model_A1, model_B1])
+    model_ab12 = compose([model_A1, model_B2])
+    model_ab13 = compose([model_A1, model_B3])
+    model_ab34 = compose([model_A3, model_B4])
+    model_ab44 = compose([model_A4, model_B4])
+
+    assert len(model_ab11.get_concepts_map()) == 3
+    assert len(model_ab12.get_concepts_map()) == 4
+    assert len(model_ab13.get_concepts_map()) == 3
+    assert len(model_ab34.get_concepts_map()) == 3
+    assert len(model_ab44.get_concepts_name_map()) == 3
+
+    # model_A1 and model_B1's respective infected compartments have same name
+    # and identifiers, they should be composed
+    assert model_ab11.templates[0].subject.name == "Infected"
+    assert model_ab11.templates[0].subject.identifiers == {"ido": "0000511"}
+
+    assert model_ab11.templates[1].outcome.name == "Infected"
+    assert model_ab11.templates[1].controller.name == "Infected"
+    assert model_ab11.templates[1].outcome.identifiers == {"ido": "0000511"}
+    assert model_ab11.templates[1].controller.identifiers == {"ido": "0000511"}
+
+    # model_A1 and model_B2's respective infected compartments have separate identifiers
+    # they should be treated as separate concepts and not composed
+    assert model_ab12.templates[0].outcome.name == "Infected"
+    assert model_ab12.templates[0].controller.name == "Infected"
+    assert model_ab12.templates[0].outcome.identifiers == {"ido": "0000511"}
+    assert model_ab12.templates[0].controller.identifiers == {"ido": "0000511"}
+
+    assert model_ab12.templates[1].subject.name == "Infected"
+    assert model_ab12.templates[1].subject.identifiers == {"ido": "0000512"}
+
+    # model_A1 and model_B3 share an infected compartment with the same identifiers
+    # "Infected" for model_A1 and "I" for model_B3
+    # since model_A1 is the first model passed in, we prioritize model_A1's
+    # infected compartment and test to see if appropriate concept replacement has taken place
+    assert model_ab13.templates[0].subject.name == "Infected"
+    assert model_ab13.templates[1].outcome.name == "Infected"
+    assert model_ab13.templates[1].controller.name == "Infected"
+
+    # model_A3 contains infected component "I" with identifiers
+    # model_B4 contains infected compartment "Infected" with no identifiers
+    # model_A3 is the first model passed in so we expect the composed model's
+    # infected compartment's name to be "I" with identifier present
+    assert model_ab34.templates[0].outcome.name == "I"
+    assert model_ab34.templates[0].controller.name == "I"
+    assert model_ab34.templates[1].subject.name == "I"
+    assert model_ab34.templates[0].outcome.identifiers == {"ido": "0000511"}
+    assert model_ab34.templates[0].controller.identifiers == {"ido": "0000511"}
+    assert model_ab34.templates[1].subject.identifiers == {"ido": "0000511"}
+
+    # model_A4 and model_B4's respective infected compartment share the same name,
+    # "I" and neither has an identifier.
+    # They should be treated as the same compartment.
+
+    # This tests to see if the two infected compartments are composed into one
+    # If treated as separate compartments, then the number of templates will be 3
+    assert len(model_ab44.templates) == 2
+    assert model_ab44.templates[0].subject.name == "I"
+    assert model_ab44.templates[1].outcome.name == "I"
+    assert model_ab44.templates[1].controller.name == "I"