Generally, no. Each manufacturer has its own internal design, stems, cartridges, handles, trim that fits their particular valve. There are some aftermarket companies that make repair parts for some of the more popular valves, but the quality is sometimes suspect. The part of a valve that is standard is where the water supply attaches, from that point on, it is all proprietary.
Plus, in the last 35-years, the technology and rules on how a shower valve operates have changed. The new ones require anti-scald technology, which yours may not have. So, it's probably time to bite the bullet and put in a new valve. If yo udon't have access from behind the wall, then there are various companies that make remodel plates that are a trim that goes behind the new valve's trim, that is big enough to cover the bigger hole you need to install the new valve from the front. I recently did this at my mother's house, and used Delta's remodel plate (which cost me about $25).