Flipping the coin.

The primary way to travel between dimensions is via a coin. These coins can have more than 2 sides, and these sides are not random. (for example it would go side A → B → C → A, etc.)
The first two dimensions the players flip between are very similar. There are minor cosmetic differences, but people are the biggest difference. How they interact and how that has affected the world differs from dimension A. All three cities are the same for the most part.
Dimension C is where things get different. In this dimension the Neuheit dam has been destroyed, taking most of the city with it. StarrWald is the primary suspect, and the two cities hold a strong grudge. Neuheit is small, but persistent at trying to rebuild. Blindport is bigger and more industrious due to many of the Neuheiters moving there. The railroad is in shambles, and there are more bandit groups. Things are on the brink of war, Starrwald determined to wipe Neuheit off the map completely. There are large parts of forest in this dimension that are torn down, as Neuheit began work on a railroad that would cut through the mountains and connect both ends of the landmass.

There are countless dimensions, but coins only take you to the dimensions assigned to them. For example, if you’re in dimension E and your coin only has A and B, it can only take you to those but will work in any dimension.

Flipping a coin will keep you in the same spot though. So if you’re locked in a room in dimension A, you’ll still be in that room in dimension B. (But the door might be unlocked).

Some dimensions are bigger than others. Some are like individual dungeons, and some are very fractured. Many of these smaller dimensions are visited via items that are not coins and are intended for one way use.

The Shattered Order.

This is a group that spans multiple dimensions. They all wear a mask, each of them with a different facial expression. The Shattered Order works to stop people from flipping through dimensions willy-nilly, as it further tears the fabric of reality and all that. The Shattered Order is in fact all one guy, each member being them from different dimensions. Though they want to stop people to prevent further damage, they themselves cause quite a bit of damage in their crusade.

The universe that is one.

This is a dimension where everything is one thing. It know’s it’s everything, it’s never known anything that wasn’t itself. So, when it learns there are other dimensions, it comes to the conclusion that these other dimensions are pieces of it. Pieces that it needs to join with itself again (can’t be broken, that’s bad!). This dimension is really fucking stuff up pretty bad, and needs to be stopped.

What’s with the universe.

Something happened that fractured the universe (well, this universe/plane of existence. The plane of fire, astral plane, etc. are just fine) Like shattered glass, fractures radiate outwards from the original breaking point. The closer to the breaking point, the more disjointed and fractured the dimensions become.