18+ Kami to Sengoku Seitokai

The "Unsinkable" Katsuragi Musashi is attending his 1st day at school, a month into the semester. He's called that because through a series of lucky incidents he has never lost a fight. Not 5 minutes into his 1st day, he's drawn into a fight to save an old friend, Kaoru. After taking down 2 guys in one shot, he is saved from taking on 6 more when the vice president of the student council and resident idol, Kagura Mami, shows up and stops it from going any further. Which is strange in and of itself since she never helps anyone. Later on, while running from his childhood friend, Akane, Katsuragi stumbles across an old school building with a mysterious large door inside, that cannot be opened. The opening of the door, this one event would change his life and effect those around him. Now suddenly, he's being named successor to the student council president by Kagura, who is now living with him and chosen students, himself included, are imbued with supernatural powers akin to animals. Also, Katsuragi now has a tail.