diff --git a/src/MOI_wrapper.jl b/src/MOI_wrapper.jl
index 0ac9e5a..c1957be 100644
--- a/src/MOI_wrapper.jl
+++ b/src/MOI_wrapper.jl
@@ -261,7 +261,20 @@ function load_objective_term!(optimizer::Optimizer, α, vi::MOI.VariableIndex)
     return addentry(optimizer.problem, 0, blk, i, j, coef, true)
 end
 
+function _check_unsupported_constraints(dest, src)
+    for (F, S) in MOI.get(src, MOI.ListOfConstraintTypesPresent())
+        constrained_variable =
+            F == MOI.VectorOfVariables &&
+            MOI.supports_add_constrained_variables(dest, S)
+        if !(MOI.supports_constraint(dest, F, S) || constrained_variable)
+            throw(MOI.UnsupportedConstraint{F,S}())
+        end
+    end
+    return
+end
+
 function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike)
+    _check_unsupported_constraints(dest, src)
     MOI.empty!(dest)
     index_map = MOI.Utilities.IndexMap()
 
diff --git a/test/MOI_wrapper.jl b/test/MOI_wrapper.jl
index f3a025a..ae78b53 100644
--- a/test/MOI_wrapper.jl
+++ b/test/MOI_wrapper.jl
@@ -36,6 +36,18 @@ function test_options()
     )
 end
 
+function test_unsupported_constraint()
+    model = MOI.Utilities.Model{Float64}()
+    x = MOI.add_variable(model)
+    MOI.add_constraint(model, x, MOI.GreaterThan(0.0))
+    MOI.add_constraint(model, 1.0 * x, MOI.EqualTo(0.0))
+    @test_throws(
+        MOI.UnsupportedConstraint{MOI.VariableIndex,MOI.GreaterThan{Float64}}(),
+        MOI.copy_to(CSDP.Optimizer(), model),
+    )
+    return
+end
+
 function test_runtests()
     model = MOI.Utilities.CachingOptimizer(
         MOI.Utilities.UniversalFallback(MOI.Utilities.Model{Float64}()),