If you liked this
Games like Rescue Pets: My ePets
If you finished Rescue Pets: My ePets, the closest matches are Littlest Pet Shop Friends, My Talking Tom Friends, Kawaii Pet to Kurasou! Wan Nyan & Idol Animal, Catz and My Puppy Shop. All 10 share its arcade genre and are ranked by how closely their themes and modes overlap.
