In my experience, payers will typically apply reductions cumulatively for every modifier and for each circumstance that warrants a reduction. So, for example, if 50% multiple surgery reductions apply and if multiple surgeries are performed by an assistant at surgery, the reduction for the modifier 80 or AS (20% or 16%, or whatever the specific payer reduction is) will apply on top of and in addition to that multiple procedure reduction. So in your situation, I would expect that any reduction for a modifier 52 or 53 would also apply in addition to the reduction applicable to a modifier TC.
However, claim reimbursement is always based on the terms of the provider contract, plan guidelines and payer policies: contracts, policies and plan documents are always your final 'source of truth'. Without knowing the details of those, as applicable to the facility in question here, there is no way to know for sure what would be the correct reimbursement - it would just be speculation on anyone's part.