diff --git a/src/Utilities/matrix_of_constraints.jl b/src/Utilities/matrix_of_constraints.jl
index 60d9f25970..13e9883c07 100644
--- a/src/Utilities/matrix_of_constraints.jl
+++ b/src/Utilities/matrix_of_constraints.jl
@@ -316,6 +316,18 @@ function _add_set(sets, i, func::MOI.AbstractVectorFunction)
     return add_set(sets, i, MOI.output_dimension(func))
 end
 
+const _MATRIXOFCONSTRAINTS_MODIFY_NOT_ALLOWED_ERROR_MESSAGE = """
+MatrixOfConstraints does not allow modifications to be made to the model once
+`MOI.Utilities.final_touch` has been called. This is called at the end of
+`MOI.copy_to` and in `MOI.Utilities.attach_optimizer` (which is called by
+`MOI.optimize!` in a `MOI.Utilities.CachingOptimizer`). In order to be able to
+apply modifications to this model, you should add a layer
+`MOI.Utilities.CachingOptimizer(MOI.Utilities.Model{Float64}(), model)`
+where `model` is the current model. This will automatically empty `model` when
+modifications are done after `MOI.Utilities.final_touch` is called and copy the
+model again in `MOI.Utilities.attach_optimizer`.
+"""
+
 function _add_constraint(
     model::MatrixOfConstraints,
     i::Int,
@@ -343,6 +355,13 @@ function MOI.add_constraint(
     if i === nothing || F != _affine_function_type(T, S)
         throw(MOI.UnsupportedConstraint{F,S}())
     end
+    if model.final_touch
+        throw(
+            MOI.AddConstraintNotAllowed{F,S}(
+                _MATRIXOFCONSTRAINTS_MODIFY_NOT_ALLOWED_ERROR_MESSAGE,
+            ),
+        )
+    end
     return _add_constraint(model, i, IdentityMap(), func, set)
 end
 
@@ -434,6 +453,11 @@ end
 
 function final_touch(model::MatrixOfConstraints, index_map)
     if model.final_touch
+        # If `default_copy_to` calls `final_touch`, then `index_map` is not
+        # `nothing` and `final_touch` should be `false`.
+        # When `CachingOptimizer` calls this, `index_map` is `nothing`
+        # and `final_touch` might be `true`.
+        # So we are always in a case where `index_map` is `nothing`.
         @assert index_map === nothing
         return
     end
diff --git a/test/Utilities/matrix_of_constraints.jl b/test/Utilities/matrix_of_constraints.jl
index ba8058edac..74f71a2fdf 100644
--- a/test/Utilities/matrix_of_constraints.jl
+++ b/test/Utilities/matrix_of_constraints.jl
@@ -510,6 +510,22 @@ function test_copy()
     return test_copy(MOIU.OneBasedIndexing)
 end
 
+function test_modif()
+    model =
+        matrix_instance(Int, MOIU.Box{Int}, OrdLP{Int}, MOIU.OneBasedIndexing)
+    x = MOI.add_variable(model)
+    fx = MOI.SingleVariable(x)
+    func = 2fx
+    set = MOI.EqualTo(1)
+    c = MOI.add_constraint(model, func, set)
+    MOIU.final_touch(model, nothing)
+    @test_throws MOI.DeleteNotAllowed(c) MOI.delete(model, c)
+    err = MOI.AddConstraintNotAllowed{typeof(func),typeof(set)}(
+        MOIU._MATRIXOFCONSTRAINTS_MODIFY_NOT_ALLOWED_ERROR_MESSAGE,
+    )
+    @test_throws err MOI.add_constraint(model, func, set)
+end
+
 end
 
 TestMatrixOfConstraints.runtests()