Shuffle!(2003)

Anime description from Froth-Bite:

The world as we know it was suddenly altered forever when the door for the dimension of the gods and the door of the dimension of the demons suddenly opened up. Ten years later, a boy named Tsuchimi Rin was entrusted with two princesses from those dimensions. Will he be able to keep his sanity while living with his childhood friend Kaede, trying to live a normal school life, and also being a neighbor to both of princesses and their fathers, the mighty dimension Lords? The hearts of those girls are at stake and only Rin has the key to unlock them.