This depends on what sorts of multiverse you are talking about. There are many contexts in physics in which the word “multiverse” appears. Check out the many types in the wikipedia page for multiverse: Multiverse - Wikipedia
If I am assuming you are talking about multiverse in the inflationary cosmological sense, then there would be as many kinds of universes as there are initial conditions for the hot big bang, as this would depend on when that particular universe bubble exits inflation. What this actually entails in terms of the kinds of Universe that we can get is a technical question that is difficult to answer. By this I mean that I can give you some examples of the different kinds of universes that one can get, but to give an exhaustive list is difficult. It suffices to say that universes with varying values of physical constants (such as the gravitational constant, electron charge, etc) are not only possible but likely.
Note that just because there are an infinite number of a certain kind of universe, it does not mean that we cannot compute how probable that kind of universe is. For example, while there are infinitely many universes that are akind to ours, the probability of our universe occurring versus a different universe (that does not support life, for example) occurring is extremely small. This is what I meant when in this thread: Is Earth a Privileged Planet? - #7 by T.j_Runyon I call the multiverse as being misanthropic.