We don't know, so we cannot answer the question, but at least we have asked the question! We have conceived of the possibility. If you state that there are or are not parallel universes what are you basing the statement on? It's like expecting the Montgolfier balloon to be as good as it will ever get. We have no idea what will be discovered next week, never mind over the next century. If there is another universe - even one - then it will require a joint effort of 16 dimensions - the basic four, four for the interface, for each universe. If there are three parallel universes, then the dimensions list gets a lot bigger. We have not yet discovered other dimensions, but we can acknowledge that they may be possible. Science is the way, the truth, and the light. It is is the only journey that we should travel. :)