@mylifeisdubbed that is a good question and the answer is . . . It depends on the AU. I have multiple that include several different iterations and they all work differently so I’ll give you a rundown.
The AU for the post this comment was left on was the Discord AU. If you've ever read a fic where one version of the turtles gets dropped into a group chat with another version of them, like The Last Ronin Becomes A Discord Admin by MelonPalooza or Too Many Turtles by DysfunctionalRequest, then you have some idea about how this works. The universes don't all line up timeline-wise so every iteration is at a different point in their story. The 2012 turtles are about 20 and have finished their S5 adventures, the Rise turtles are somewhere between finding out about the dark armor and S2 finale, and the Bayverse and Mutant Mayhem movies haven't even happened yet. Through this group chat, after a few initial mishaps, they help each other manage the shenanigans their different universes put them through. I will say that through science and mystics, multiple iterations do physically meet later on in the story but saying anything more would be spoilers.
The disc fic includes Rise, 2012, 2003, 2007, Bayverse and MM/Tales. It's one of the simpler multiverses.
Another easy one to explain is Kappa Kafe. Kappa Kafe is a fan iteration where a band of spirits (this iteration's turtles) that live in a sort of limbo between worlds operate a rest stop for people from different universes. The initial idea was a coffee shop kind of a deal but it's since expanded to a small neighborhood where turtles of any universe can take a breather before getting back to their canon lives. There's no pressing story taking place here and it's open to interaction so it's perfect as a backdrop for crossovers and AU doodles. Any iteration can be thrown into this, including fan iterations.
While we're talking about crossovers, one of the multiverse AUs, Legend of Turtles, is a crossover with Legend of Zelda. Every Zelda game has a different TMNT iteration paired with it and the turtles act as companions for Link, Zelda, and depending on the iteration & game sometimes Ganon. Right now I'm focused on Rise with BotW and related games, and 2012 with OoT, MM & TP. In these ones, the turtles are split up and join Link and their brothers as Link travels across Hyrule, but in others they're together from the start. The brothers usually join the Zelda world as children and grow up alongside Link & Zelda, but they remember some things from their original world.
In BotW, Leo is paired with Link and is the one who originally brings him to the Master Sword. Donnie is Mipha's companion and the first to reunite with Leo but he doesn't join the party until Link recruits him after the 100 year nap. Raph was taken in by Daruk and after the 100 year nap mentors Yunobo. Mikey is found by Revali who comes to think of him as a brother and becomes jealous when Leo comes around with link and Mikey immediately gravitates to Leo. This stuff isn't relevant to the multiverse bit, I just wanted to include it.
I might do a Links Meet situation including all the different versions of the turtles, but I don't think it'd be a full-fledged thing because that's a lot of people to keep track of in one situation.
CRASHOUT is a multiverse fan iteration I briefly explained in this ask about Venus but I'll explain it in more depth here. While it is it's own iteration, the canon TMNT iterations tie into it via. Well. Ghosts. Kind of.
There are a few kinds of speculative multiverse theories, but the one I like to use is about soap bubbles. Imagine the multiverse as a massive bubble bath. Every individual bubble is it's own universe. When two of these bubbles rub together, it triggers connected events in both universes. The CRASHOUT universe is one big bubble, and canon iterations are smaller bubbles that cling to it, and where the bubbles join the universes start to bleed together. These bleeds manifest in the counterparts from these various universes (recuring characters from different iterations like the turtles, April & Casey, Splinter & Shredder) starting to blend into their counterparts from the CRASHOUT universe. The CRASHOUT characters can use this blending to access the physical and mystical abilities they have in canon iterations, but this comes with the downside of ghosts of these counterparts hanging over them.
Pros: Superpowers and ninja skills to help the average high schooler survive the apocalypse! Cons: There's like seven alternate yous haunting your ass and they're all shitheads.
CRASHOUT includes every iteration I have or will soon watch, including Rise, 2012, 2003, 2007, Bayverse, MM/Tales and the IDW comic run, plus the original cast of the fan iteration.
And then, most complicated of all to manage, we have the absolute unit of an AU that is Body Brothers. In Body Brothers, all of the turtles in every iteration I have just listed above (minus CRASHOUT) mind swaps into different universes at random to help each other. I have no plainer way to explain this. They switch bodies with their alternate selves at my every whim, not even because of magical mishaps, just, they just do for their entire lives because why not.
I love Body Brothers conceptually, I do, but it is a massive thing to coordinate and keep track of timelines for. They all need nicknames and identifiers depending on who's in who's body and there are seven iterations in this bad boy, that's twenty-eight turtles at the very least all switching around and adapting to seven different worlds and I promise, I promise I will make charts and spreadsheets and release them into the wild so everyone can understand who's who but it's gonna be a hot minute.
I suppose Scattered Songbirds might also count as a multiverse, but it's specifically a Rise multiverse. SS!Leo and SS!Mikey open portals to different Rise timelines to help the turtles in these timelines and sometimes bring them home with them. It's not dissimilar in concept to @dreamweave01's Woven Ties AU (which is AWESOME and I recommend checking it out if you haven't along with their other art) but is wildly different in execution as it's based entirely on a random dream I had.
And those are all of my multiverse AUs as they are today!