Midoriya Doll Quirk AU
Let me elaborate on his quirk.
Midoriya can both create voodoo dolls that actually work (if you were to stab the doll in the leg damage would be inflicted on the real person, can manipulate a person's movement using the doll, etc.)- he can manifest these after contact with a person (has to be all five fingers on a person and he must be touching the person while manifesting the doll in order to form the link)- and turn someone into a doll (also five-finger activation and he must be touching the person), which takes longer than making a voodoo doll (2 minutes compared to 45 seconds). He can also turn himself into a doll, but he can only stay in the form for up to two hours. If the doll takes extreme damage- an arm or leg getting pulled/cut off for example- he will feel the pain of that happening to him and when he transforms back he will begin to cough up blood as well as have blood leaking from ears, nose, and eyes.
In this AU, most of Hisashi's side of the family have doll/toy-related quirks, with Hisashi having a quirk that allows him to make a link with people through eye contact and channel it through dolls to control people. In this, Shinsou is Midoriya's cousin on his father's side.
Inko's side of the family has a history of five-finger activation quirks. She's also Nana Shimura's daughter and Overhaul's half-sister. This makes Shigaraki and Midoriya cousins, and makes Eri distantly related to Midoriya through adoption. I also meddled with Inko's quirk a little so she also has a five-finger activation quirk. It's basically the same as her gravitational quirk in the show, she just has to touch the object with all five fingers first.
Overhaul's biological dad (we're gonna call him Akui Kai) had a fling with Nana while he was married, and Nana gave birth to Inko because of it. Akui's wife (Satsujin Kai) found out about his cheating and killed him, then put Overhaul up for adoption and killed herself. Nana and Akui had a falling out and cut off contact with each other just before Inko was born because Nana found out he was married.
Shinsou is Hisashi's nephew, but Hisashi didn't have a good relationship with his sister (Shinsou's mom) and they didn't speak with each other. He doesn't know she's dead. Their falling out was over Shinsou's father, who was a villain and wound up killing Shinsou's mom. Hisashi knew he was a villain and tried to get his sister to leave him. Shinsou's dad killed his mom when she found out about his being a villain. Shinsou's dad (Shi Shinsou) was killed by Endeavor. Shi had a quirk that was called "Puppeteer" and allowed him to control someone's body once he ingested their blood. Shinsou's mother (Asumi Shinsou) was able to turn people into dolls once they answered a question, and once the doll was injured or she wanted them to, they turned back.
Midoriya's quirk was considered villainous by most, but Bakugou continued to be friends with him, labeling him a villain too. Midoriya is one of the only people capable of calming down the angry Pomeranian. Toga transferred to Aldera in their second year of middle school and became friends with Midoriya. After finding out about Toga's home life, Inko (a lawyer) took her parents to court and adopted Toga, who became Himiko Midoriya. Midoriya also met Kouta and Eri earlier than in canon. Muscular attacked Kouta in an alleyway when he tried to run away from Mandalay. Midoriya stepped in and became Kouta's hero. He babysits for Mandalay often and is Kouta's unofficial big brother.
He met Eri in a different way than canon. Overhaul discovered he had a half sister, and decided to get in touch. He tried to manipulate Inko into helping him with his plans by being Eri's caretaker. Despite not being able to do much against Overhaul herself, Inko told her son about Eri and helped him sneak into the Yakuza. He took Overhaul down and saved Eri singlehandedly. They then adopted Eri.
Then Hisashi tried to get in contact with his sister, only to find she had died and left behind a son who was in a foster home. Shinsou had been labeled a "troubled kid" because of quirk discrimination. Hisashi immediately adopted him. Their conversation when Hisashi took him home went something like this, I imagine:
Shinsou: Why would you adopt me?
Hisashi: Kid, it's not my first time doing this. I swear to God Izuku brings home another kid each week. Besides, I'm your uncle.
Shinsou:... What?
Hisashi: Your mother was my sister. We had a falling out while she was pregnant. I just found out she was.. you know... when I tried to get back in contact with her.
Shinsou: Did you know about my dad?
Hisashi: Yeah. I tried to get her to break up with him so she would be safe, but I tried to do it without telling her he was a villain. If she knew he'd have to kill her. But she was adamant he would never hurt her and cut contact with me.
Shinsou: Who is Izuku?
Hisashi: My son. You'll meet him when we get home.
Shinsou: Is there anyone else?
Hisashi: Oh definitely. My wife Inko, our oldest adoptive daughter Himiko, our youngest adoptive daughter Eri, that Kouta kid I'm pretty sure Inko wants to adopt who Izuku keeps babysitting, and Katsuki who doesn't technically but might as well live with us. He's Izuku's... something. Not really sure. Oh! And Mei. I think Inko wants to adopt them too. They're Izuku's best friend. I'm sure there'll be more eventually.
He was correct. At school, upon meeting Uraraka (who lives alone to help out her parents) Midoriya decided he was his newest sister and somehow Inko wound up with custody over her. They proceeded to do this with Todoroki, Tokoyami, Dark Shadow, and Hawks (He interned with Hawks instead of Gran Torino in this, because he doesn't have One For All). Also, in this he followed Bakugou into the portal at the camp so they were both kidnapped. The following interacting went something like this:
Midoriya: I think we have enough room in our house.
Bakugou: One, I don't live with you, and two, NO.
Midoriya: I'm sure mom and dad will be willing.
Bakugou: You can't adopted every single traumatized person you come across-
Midoriya: Of course I can't, that would be impossible. But I can adopt these ones.
Shigaraki: What in the-
Obviously, Midoriya had his way and the Midoriya family had six new members.