You get into string theory, and you get several more dimensions that a lot of people are aware of than four. The first four have one word names literally: length, width, depth, and time of course. Anyway, there's too much that happened in Star Trek's world with Kahn Singh and the eugenics war in the 90's but never in the Earth world's history. There's so much fantasy technology that we're never gonna get. Even if warp speed alone was possible, there are sublight speeds are extremely stressful for me to think about traveling at because of the extra G forces, and that's why I've only been on one roller coaster that was a little kid one when I was one. Then you get people and an android who saw Spock do the nerve pinch where they touch people's shoulders, and they're down after their hands are removed and able to get up later. Beaming's never gonna happen, and that sounds like the least stressful way to get around. If you go by the canon universe in Star Trek, they've dealt with one of the string theory dimensions that accounts for other worlds with those mirror episodes; but aside from giving dudes cheap thrills in the Kirk and sooner stories, those ones are ones I don't care for. Here's a quick run down on three more dimensions that I found on Google.

5 other worlds (parallel naturally)
6 plane of all possible worlds with the same start conditions
7 plane of all possible worlds with different start conditions (for instance Eve resisting temptation to eat from that forbidden fruit)

No parallel worlds will be possible to travel to without God's supernatural powers according to what anything I've read on those.

Take care and God bless