In my head, I assume most fiction is already parallel universes of each other. Explanation could be we‘re on a branch of the multiverse where Earth and Humans usually exist. Physics differ due to the absence/presence of subspace and hyperspace in each universe and their properties.
As I said, parallel timelines of the same universe would have to have the same physics, because they'd branched off the same origin. Obviously any two universes that had humans in them, that have a common human history and culture, would have to have diverged after humanity and those common historic and cultural antecedents arose.
After all, if the laws of physics were even a tiny bit different, if the values of the fundamental constants were changed by even a fraction of a percent, stars, planets, and matter as we know them couldn't exist, so life certainly couldn't. Different fictional universes can independently posit different hypothetical physical laws beyond the known ones that allow matter and life to exist, but they just can't plausibly go together as parts of the same multiverse. They're just independent works of imagination that set different ground rules.
And yes, somebody always drags out the old saw, "Well, if there's an infinite number of random universes, then it's probabilistically inevitable that every possible reality will exist somewhere, so universes that are exactly like ours down to individual people but with different physics are bound to exist." But that's an abuse of the concept of infinity. If there's an infinite number of universes, the odds of ever
finding one of the X universes that had duplicate people in it would be X divided by infinity, which is zero. In other words, it would take an infinite amount of searching to find any of them. So even if they did exist, the probabilty that any two of them would ever interact is zero.
Of course, you can always just throw out logic and intelligence and mash up any two universes you want as a fantasy premise. But different universes have different degrees of plausibility, and I don't like lowering the standards of a more plausible universe (as
Star Trek was originally intended to be, though that keeps eroding) to the level of a more fanciful one. I can buy, say, the Arrowverse crossing over with
Smallville or
Lucifer because it's a fantasy universe to begin with (although even there, there are details that bug me, like the totally different rules for angels between
Lucifer and
Constantine, or the fact that Kryptonians can fly and breathe in space in
Superman & Lois when they can't in
Supergirl). But I don't want Trek crossing over with a less plausible universe.