I haven't played the game yet, but I vaguely remember from reading reviews that this Japanese adventure game may play with a many-worlds interpretation:

http://en.wikipedia.org/wiki/Zero_Escape:_Virtue%27s_Last_Reward

Thanks for reminding me about this. I don't think I owned a Vita when I originally heard about it. I should be able to play it now. Is that the sort of game you were thinking about?

Limiting how far 'sideways' you can go in one jump might at least keep thing under control (how much you have to rebuild of the game world)

Having a system where (everything/some) is rebuilt seems a given for such a game. Doing this with a NON mutating multiverse is already hard enough.

Limiting the scope of what can bee seen (and in what detail) of the game world is also something that might be needed. Worlds with 'societies' the player deals with bumps up the complexity quite a bit.

Of course you could just precan much of the possible worlds (so they will be cohesive and make sense within themselves)

Bioshock Infinite went fantasy with a pseudo-gibberish multiverse system they didnt even apply consistantly and it resulted in a contorted plot mess many players just said 'Uh-huh, Thats nice. Now can I get back to the shooting..." (Note - that was all precanned with no real divergent 'realities' options)