About the question posed by OP:
Nothing would happen really, there doesn't appear to be a way that our universe can interact with parallel universes, if any, on an observable level, if it exists.
However,
Something that I read recently suggested that evidence from WMAP data may reveal to us that the universe takes on the shape of a dodecahedron massively large across (much farther than presently observable) with a finite size but has the shape of a torus on a 4-D plane. Basically, our present world may be sufficiently "reflected" in all directions billions and billions of light years away, that might constitute as a parallel universe, since its elements are all the same as in this present universe. But if we were to be able to observe it directly, we'd be looking billions and billions of years into the past, regardless of direction.
But more relevantly, M theory has roughly 10^500 solutions, where each solution is a unique universe as I understand it. One of these universes must be that I live happily with a harem of a bunch of women whom I love and who love me.
So where the hell is it?