Are some brands of shower valves compatible with others?
I have sort of done this with an American Standard shower valve. There's three parts that need to be adapted. The trim ring is the easiest. Get a piece of aluminum plate, 1/8&quot; is a good size and cut a circle large enough so it fits over the shower valve. Cut the outside so it fits in the hole in the wall. Match it up with the correct plate for the valve and mark it where the mounting screws are. Drill holes in that location just large enough so the mounting screws will go through. Now get the right length/thread screws and mount this plate to the valve. Now take your new trim ring and line it up and and mark where the screws hit the plate you fabricated. Drill and tap the plate you fabricated for the mounting screws for the new trim ring. Your new trim ring will fasten to this mounting plate.
As far as the trim tube that can be held in place by the trim ring. You should be able to silicone the trim tube to the trim ring which should hold it.
As far as the handle that's where you'll probably have some trouble. You'll need to go online and look at installation instructions to see if there's any that have the same mounting method, my guess is you'll strike out on this part.
Easiest thing to do is to look for a universal black shower trim kit. It should come with all the adapters.