find -name "*.xyz" -o -name "*.abc" -exec to Execute on all found files, not just the last suffix specified

I'm trying to run

find ./ -name "*.xyz" -o -name "*.abc" -exec cp {} /path/i/want/to/copy/to

In reality it's a larger list of name extensions but I don't know that matters for this example. Basically I'd like to copy all those found to another /path/i/want/to/copy/to. However it seems to only be executing the last -name test in the list.

If I remove the -exec portion all the variations of files I expect to be found are printed out.

How do I get it to pass the full complement of files found to -exec?