The Curt Class II Trailer Hitch Receiver # C12005 referenced in your question is confirmed to fit your 1988 Oldsmobile Cutlass Supreme Classic with RWD. This Class II hitch has a maximum tongue weight of 350 pounds and a maximum trailer weight of 3,500, although I recommend also checking the vehicle's capacities as listed in the owner's manual, as this will most likely be the limiting factor. This is a custom-fit trailer hitch so no drilling will be required during installation. I have... view full answer...