It will surprise you to hear, just as it suprised me, that MWI and Copenhagen have been axiomatically identical from day one. I know what you are thinking, something like, "if the problem was closed we wouldn't be talking about it, so it must be open." Yeah, well...

There is a list of axioms of quantum mechanics, Copenhagen and MWI disagree only on how you get to them. (And also on their conceptual interpretation). That's why they're called interpretations of quantum mechanics, not theories of quantum mechanics.