You can start keeping track of the additional expenses. Child support isn’t limited to that ordered by a court but what you actually pay. If the child lives with you, he lives with you. It doesn’t matter if H doesn’t take him on taxes as divorced parents can take the deduction whether or not the child lives in the household.
If you pay for a sports league or a school trip that is above the normal child support, keep track of it. Orthodontics or other medical expenses? Write them down.