Ok, so i've thought of three undertale/tmnt crossovers, one of which will likely have a lot to do with another.
Overshell-- (originally Undershell, but choosing to use that title for a different au) an au in which Frisk and the underground monsters meet the tmnt and co. The tmnt try to convince the monsters to stay away from humans, Frisk makes it their #1 goal to bring monsters, humans and mutants to unite and live peacefully together. Needless to say, many mutants have their doubts on how possible this is.
Undershell-- somehow the Kraang manage to chase Master Splinter out of the city instead of into the sewers. The chase him up Mt. Ebot (which is actually not supposed to exist in that earth, in any of them, but more on that later) and in a last-ditch attempt at protecting his boys and himself, leaps into the hole to the underground.
The Kraang, of course, follow him in and there he is aided by Toriel, caretaker of the ruins. After defeating the Kraang, Toriel takes Splinter to her home where they have a good long talk about how he ended up in his situation, about the underground, etc. Somehow Toriel finds out about his human soul, (having assumed he and the tots were fellow monsters before) and tells him he can NEVER reveal his soul to anyone, or else he'll be hunted and killed.
This all takes place 13-14 years before Frisk's arrival, so still some time before the events of tmnt 2012 begin. Toriel helped the Hamato clan get into the legal system records and thus Splinter was able to open up a dojo either in the city or in a small town unreachable to Frisk during the main game.
The boys grow up believing they're all regular monsters and Master Splinter becomes somewhat reclusive, not really speaking to others very often aside from his sons, students and parents of students.
Of course, this doesn't last forever and the boys do end up having some contact with Frisk and the rest of the main cast.
Also: the brothers find out that not only are their souls neither monster nor human, but also that that can easily pass through the barrier on their own, something they unanimously decide to keep to themselves until they figure out why.
Endingshell-- the last and probably final of my ut/tmnt aus, mostly involves my outcode Donnie, Static!Donatello.... Which is still pretty under developed. But basically, he keeps trying to save Mikey, who's been possessed by Chara, but keeps failing. He resorts to going from au to au stealing human and animal mutant souls alike in an attempt to become a god and save his bro. He's also got a huge soul-separating machine he's building in the anti void. (Being in the anti void also is slowly eating away at his sanity. He continuously keeps rejecting the kind offers of company and hanging out of the kinder anti-void residents. I.e, Core Frisk.)
The main souls he's after are kindness and integrity souls.
He combines his power and knowledge with a Gaster's soul, giving him many of the same abilities as Sans. I.e, teleporting, gaster blasters. But he does not have the Karma ability, however. This team up happens after Gaster and Static!Donnie make a deal of some sorts.
Donnie cannot use gaster blasters without the use of Gaster's soul. Solo, Static!Donnie can make machinery glitch out and anything with speakers or screens produces mostly static when he is present. Thus where he gets his name.
Static!Donnie is an adult, not a teenager. He tends to take the shape of a slightly older version of whatever Donatello resides in whatever au he's in. His true form, however is somewhat melted looking and skeletal, with glitchy code bits like Error Sans and Geno Sans.
Speaking of which, Error naturally considers him to be an abomination and wants him and all the tmnt au's destroyed. Ink however, is fascinated and even excited at the idea of these new, strange au's he never new existed. It's like he's been given access to a whole new multiverse! (He has)
That's all I'm gonna write about Endingshell, Undershell and Overshell for the time being. It's 1:40 am and I'm exhausted.