If you're looking for manga similar to My Animal, you might like these titles.
One day, Hirari Yumesaki awakens to a text message from "God" saying that in one year, he will be sending an enormous meteor to destroy the Earth, and that he will give her a different supernatural ability each day so she can test which may have a chance of preventing armaggedeon. But despite the hilarious situations that her ever-changing abilities bring, along with an ensuing love triangle, will she and her "ability mentor" Kaname Mito be able to use these powers to stop the meteor and save the world?
As a young boy, Chiaki Mikado had an encounter with an unusual, three-headed puppy, and as a consequence of a bite from that dog, he lost a piece of his soul. Now a teenager, he finds himself unable to enjoy anything, but the three-headed dog is back in human form -- or more accurately forms -- to fix all that! Turns out that the three heads of the mythical guardian to the gates of the underworld are actually unique individuals, and each a pretty young girl at that! With his new roommate(s) leading the charge, can Chiaki experience the happiness that has so long eluded him?
Fifteen years ago, indiscriminate supernatural attacks rocked Japan-prompting the government to create the Tactical Raveling Unit in the First Counter-Psychotrauma Division of the Special Measures Agency…or TR1M, for short. Their purpose? To deal with the monstrous manifestations called the Unraveled. And they’re good, too… so when TR1M agent, Raveler Second Class Nika Ago, is shipped to a far-off backwater, she knows her poor performance is to blame…but what she doesn’t expect is to find a hotbed of Unraveled activity, and a boy with a secret who just might be her way back into TR1M’s good graces!
In this world, there are those who look like humans but are actually beings with supernatural power. In order to respond to crimes committed by these kinds of people, an organization that employs some of their number has been established. Kurohimeyama Eve is a member of this organization, and she is also a teenage girl that has "Oni" powers. One day, she goes to meet a new member, Ichizuka Senya, who is a boy with dangerous shadow powers and a bad personality. In front of the other girls in the organization, though, he seems to act perfectly nice. What's even worse, he's transferred into her private religious school! Kurohimeyama's once-peaceful life will never be the same!
Kasane are spirits who latch onto the shadows of people's hearts. But as long as Yayoi and Aoba are around, evil spirits won't be hurting any students at the school! Beautiful art and occult action! The door to the unknown has now been opened...