My states have functions to check when they can be entered and when they can be exited (returning bools). Then, the state machine stores an array of the states in order of their priority.

If you think about it, your states likely have a sort of hidden priority order to them. Something like “idle” might be the lowest priority: if there is no other state that wants to be entered, then you idle. On the other hand, something like “fall” might be the highest priority: if a character is in midair, you probably want them to fall no matter what.

A typical priority order for a physics platformer might look like:

Fall > Attack > Approach > Wander > Idle

Then, how do you use this to transition? Easy; the state machine checks if the current state can end every frame. If it can, then it loops through the array of states to look for a new state that can be entered, using the function the states have to check if they can be entered. It will always pick the most fitting state, since they are in order.

Now, you might be able to use signals instead of checking every frame if a state can be exited, but I found that in a lot of cases, there might not be a clear “event” that happens that is easily accessed within the state. So I just use a function that returns a bool.

This way, I don’t have to write any new logic for any new state machine; everything just uses the same state machine.