Right. This already narrows it down, since we know you don't mean the many-worlds interpretation of quantum mechanics.
So let's look at this definition. It talks about the multiverse comprising of multiple 'universes', and also being 'everything that exists: the entirety of space, time, matter, energy, the physical laws and the constants that describe them'.
Taking the same source for our definitions (i.e. Wikipedia), we look up 'universe', and we see that it's: 'all of space and time[a] and their contents'.
This should give one a pause, since it's contradictory - everything that is cannot be a part of something else. They appear to be describing the exact same thing.
So if we want to talk about the multiverse, we need a different definition of what this sub-component called 'universe' is. For example:
1. Each observable universe (this one is stretching it, but for the sake of argument let's keep it).
2. Each currently non-overlapping observable universe.
3. Each causally separated patch of space (=observable universes that will never overlap).
4. Each patch in inflating space that stopped inflating and undergoes regular expansion.
All of these are just from the standard model of cosmology (with inflation). More definitions are possible if one's thinking about some other cosmologies, branes or whatnot, that I know little about and will not comment on here. The point is, the list is not exhaustive. (I can see now that the Wiki article talks about those in some more detail)
In each of those four cases, an argument can be made that each one describes universes that are in one way or another separate, and together form something that could be called a multiverse. Each next case is just the previous one, but that has been more restricted. So 2 is a special case of 1, 3 is a special case of 2, and 4 of 3.
As we go towards 4, the distinction between separate universes becomes less trivial, while our confidence that those other universes (and by extension, the multiverse) exist becomes less solid. But, we always have some good reasons to suppose their existence, and the choice to favour one definition over another is to a large extent arbitrary.
Furthermore, even if you pick the most restricted definition (4), and which is probably the most often referred to as multiverse of the four, you're not talking about there being some 'nothing' outside our universe (as defined). You're basically just saying that the universe is in some sense larger than what you see, so you need to update your old definition of 'everything that exists' to be more inclusive.