A lot of science or cosmology is based on the concept that "If it can happen here, it can happen somewhere else". Why not apply this to the universe itself?

The simple reason for the multiple universe idea is that it removes the fine tuning problem.

If this seems too speculative, consider that the fine tuning problem itself is really a philosophical question - you are asking why all the physical constants are at those particular values rather than other values - you are asking what mechanism defined those values - you are asking about the mechanism responsible for our universe being the way it is...

We now have a few contenders in cosmology that might take the time-line back further than the beginning of "our" universe, things like M-theory and Loop Quantum Gravity, but we have no way so far to test these ideas and they only take the "mechanism behind" question back along the time-line with them anyway.