Can the multi-verse be infinite

Answer 1

Seldom does the concept of infinity apply to real things - it is a mathematical concept. '~a number large beyond measure'. For real objects, 'arbitrarily large' is usually an adequate descriptor.

In our universe, there are about 10 to the power of 80 particles - demonstrably a number well short of mathematical infinity. Even adding a few orders of magnitude to allow for dark matter does not add all that much!

Number concepts such as googol and googolplex are still well distant from infinity.

So it may be more comfortable to use the idea of 'arbitrarily large'.

Perhaps more to the point: we don't know what the "multiverse" is. Some cosmological theories posit that there's more to "everything that exists" than the observable universe, but by definition we don't know (and quite probably never can know) anything about it. The universe itself may be infinite ... we don't know (and probably can never know, since by definition we can't observe anything outside the observable universe, which we know for certain is not infinite). If there are "other universes", there may be an infinite number of them, or there may not, we don't know.