It is canonical that there are multiple universes, and that everyone in the story is aware of them. The universes go by numbers, and the universe that Ace lives in, is Universe 7. The Universe in which the Regal Empire is in, is Universe 8. There are 40 Universes total. There are parallel universes, but their technology at the present is not able to travel to the other.
The only way in the story someone travels to a parallel universe, is through Lush, the god of Beauty of Choice.
Rules
You cannot travel to a universe that is not next to the other. For instance, a person in Universe 7 could travel to 6 or 8, but not 5. This is because of the way the worm holes connected to universes are, and because of each universe's laws of physics. The universes next to each other have similar laws of physics, but the further one gets, the more different it would be.
If one did manage to get from Universe 7, to say, Universe 20, it would be an incomprehensible sort of sensory experience and distortion of their known reality, and they would most likely die, as their own make up and structure would not exist in such a different universe, with such a rapid sudden change.
You cannot travel to a parallel universe that is not in one's own. For Example, Ace travels to a parallel universe 7 in which the genders of the characters are different. He could not, however, be in his own original Universe 7, and try to travel to the parallel dimension of Universe 8. He could however, go from Universe 7A, to the parallel Universe 7B, and then to Universe 8B.
You can affect other universes. You can affect parallel universes, and dimensions as well. The consequences can be good, bad, or neutral.
Each universe has its own laws of reality, therefore some truths in one different reality would be fiction in another. In Universe 7, magic was the work of fiction until those from Universe 8 came, and introduced it to them. They influenced another Universe, but it was only possible because their laws of physics and reality were not too far apart.
A person inside a Universe does not exist at the same time as their other self does in the next Universe. This is self correction, and prevents time paradoxes. This means, for instance, Person A in Universe 7, could not exist at the same time in Universe 8. They could, however, exist at a different time in Universe 8.
Travel through universes is only possible through wormholes. Travel through great distances in the same universe is only possible through wormholes as well.
There are gaps between Universes, and it is unknown how to get there.
Dimensions are different aspects that affect one Universe, but not another. Think as dimensions as functional parts of Universes. Each parallel universe has its own dimension that helps it function as well. They only affect the Universe it is attached to, but this can easily change. It is the one rule that can "bend". If someone from Universe 7 were to bring an aspect of one of their dimensions to Universe 8, it would affect it. This is how the Regal Empire had changed Universe 7 with the introduction of magic.
Some dimensions of Universe 7 are Heaven and Hell, respectively.
Some universes have a god/goddess, multiple gods, or none.
Universe 7 has a God, but he doesn't like to come around and meddle with free will. Universe 8's gods love to bother everyone and anyone, and Infiniti makes it quite clear.