Oh, what a great question. There are many possible scenarios for the end of the universe and scientists debate this a lot — there’s lot of speculation but it’s safe to say we don’t know whether we’ll have a heat death, big crunch, big bounce, or, indeed, if we’re in a multiverse. So my answer is I don’t know!
I agree with Catherine and Philip, not only do we not know how our universe will end, we don’t know if we’re in the only universe or not. And it’s really hard to know if another universe will end if we don’t even know if it exists!