The queston I have for multi-verse proponents is where does the energy come from?
My very rough understanding (I am far from an expert of QM or any multiverse stuff) but from Carroll's "Many World" interpretation, the idea is that the whole multiverse isn't "duplicating" or "multiplying" or anything, it's simply branching, which means that there isn't more or less energy pre- or post-branching, it is simply just "bifuraced" or, as Carroll himself sometimes puts it, the Many Worlds are "slices" of a very, very "thick" universe (or meta-universe, if you want, Carroll doesn't call it that, I don't know what he would call the whole thing). Apparently there is math to back this up, but it's Penrose-like stuff that I can't even fathom.
I think there might be a notion of that it is finite, in a way, but the number of possibly sustainable branches is something absurdly huge.