Sayori na Parallel

Okajima Sayori tripped down a flight of stairs and suddenly found herself in a parallel universe, with no idea what had happened. But she was rescued by a young man and his cat and he found a way to return her back to her own world. But instead, she finds herself traveling from universe to universe, from the medieval to the futuristic, and in every case there is a version of this man and his cat! Will Sayori ever make it home again?