There has been a good deal of research into such ideas... the first stumbling point is semantic, what exactly distinguishes multiple universes from one larger universe. I'm only familiar with eternally inflated (multi)verse theories--so my response will be relative to those.
A 'universe' (in this context) is a causally isolated region of space, i.e. it has an event horizon. This is consistent with observations, as we believe there is an event horizon at about 13.7 billion light years from us. According to eternal inflation theories, there are an infinite number of other universes out there, outside our horizon, separated from us by normal old space (which may or may not be rapidly inflating---causing or perpetuating the horizon at some point in history). There would be no 'barrier' per se, but the gap is fundamentally untraversable.
Again, I'm not very familiar with most other multiverse theories, but presumably our 3+1 dimensional universe is embedded in a higher dimensional space, and thus a 5th (e.g.) dimension separates numerous 3+1 dimensional universes... perhaps.
Hope that helps.