More than you had hoped to be
33 parts Ongoing Mature(Note: I do not own this story it is from ao3 by daylightbreaks )
In another world, Chisaki Kai is a ruthless, cruel man who stops at nothing to rid the world of quirks. In this one, however, he draws lines: one being Eri. He cares for her, treats her like his own daughter. And for his precious daughter, he needs somebody to help care for her, somebody who isn't one of the Eight Bullets or a member of the Yakuza.
Enter one Midoriya Izuku: quirkless, protective, and the perfect candidate to be her babysitter. Now if only Chisaki could just stop worrying about the boy, too, that would be great. (No, Chronostasis, he does not have 'paternal instincts,' thank you very much!)
Or: Midoriya Izuku (accidentally) turns the Yakuza into the good morally grey guys.