maybe?
4 stories
Our System Is Family by KiraRuna
KiraRuna
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    Parts 40
Izuku's head works diffrently from the rest, that wont stop them from achieving their goals together, as a family unit.
Son of the Greatest Swordsman by Stillwell03
Stillwell03
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    Parts 77
'Power only acknowledges power and ignores the weak.' These were words Izuku held close to his heart growing up. Because of this, Izuku had trained as hard as he could to gain the attention of the only man he wanted to acknowledge his existence. Dracule 'Hawkeye' Mihawk, aka the Swordsman Hero Crossblade. But what happens when the two finally meet, see for yourself. I do not own any of the art work in this nor anything else except the idea. MHA is rightfully owned by Kohei Horikoshi and One Piece is rightfully owned by Eiichiro Oda. Please support the official releases.
Need You (ShinDeku)  by _Hybrid_Wolf_
_Hybrid_Wolf_
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    Parts 128
All Midoriya wanted was to visit his mother for the weekend. Instead he's kidnapped by one of the most prominent villain groups in Japan, and they go by the name League of Villains. Back at UA, Shinso is finally going on his first hero mission as an apprentice to the one and only pro hero Eraserhead. There's just one problem. His first mission is to rescue a student that's in the hero class he's been trying so hard to get into. The boy he once looked up to, who shone so bright he seemed nearly untouchable, is now reduced to a vulnerable, traumatized teen that he's been tasked with taking care of. WARNING: In this fic some of the characters have a lot of trauma, and there will be some graphic chapters towards the beginning, though I tried to keep it to a minimum. There will be mentions of SA, psychological and physical abuse. I put warnings at beginnings of chapters, as well as the specific part of the chapter that may be triggering, when applicable. My update schedule is every other weekend. Disclaimer: I do not own any of the pictures in this book (including the cover). The characters in this book belong to Kohei Horikoshi, the writer of Boku no Hero Academia.
I Don't Run An Orphanage! by Moon_kookei998
Moon_kookei998
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Izuku Midoriya, couldn't be a hero. But despite this, he soon finds he's a magnet for trouble, particularly trouble involving children. There a lot's of children in the city with quirks that cause issues for them and the people around them. And if their parents won't care for them then he will! It may not have been the type of hero he wanted to be. But he's a hero none the less! Author:Kyodon You can also find this fiction in https://m.fanfiction.net/s/13626213/63/ and at https://archiveofourown.org/works/27421528/chapters/67028365