Bought Glass Empires recently, and my thoughts turned to the Mirror Uni and its alternates.
Imagine a Mirror, Mirror universe, like the one in Dark Mirror, where the Empire never fell (maybe Spock was stopped from causing the damage he did, or the TOS crew didn't turn him in this reality): They have been looking for ways to access this "weaker" universe, since they figure it would be much easier to conquer them. But instead of the 'mainstream' Trekverse, they stumble upon the Mirror universe of the Klingon/Cardassian/Bajoran Alliance instead. They are appalled: bad enough a world where Terrans treat "aliens" as equals, but a world where they are SLAVES!!! Being aggressive, hate filled fiends that they are, they attack.
Now, what does that mean to you and your crew of the U.S.S. Victorious? Well, what the warring universes don't know is that they are causing significant damage to the "fabric of reality". I would say leave this up to your GM: maybe ships from various alternate realities are popping up; maybe your ship is pulled into their reality. You could go the Comic book route and have a Q (or an El Aurian, if you don't have your own Q) warn the cast about a threat to "the entirety of existance". A really evil narrator would have both sides fighting in the main Trek Universe (we would be halfway between them, sorta).
Lots of interesting oppurtunities: Your heroic Captain could see himself as both a sniviling slavish coward and a viciously cruel Admiral (especially if he had always wanted to be an admiral). Titanic space battles against various species (Terran Devestator class Ultra-Destroyer versus the Alliance Drednought Kayless vs one Defiant class escort!)
The solution could be as simple as closing the sub-space ruptures they are creating, or as hard as negotiating a cease fire. (Seriously, closing the ruptures would be way easier: Intendent Worf will kill Supreme Admiral Picard for keeping his counterpart as a cabin-boy).
OH, and one little thing that I've used before in alternate reality based play. While it's true that in a uni where the Voth stayed on Earth mankind would never have evolved, so there wouldn't be alternate versions of your characters, but I came up with a semi-metaphysical loophole in that.
I came up with the idea of counterparts: it's kinda hard to quantify, but imagine that the essence of what you are, your soul for lack of a better word, is what makes you, well you. Forget about genes and heredity and all our science. So, in Voth TOS, there is an swashbuckling commander with an eye for the female saurians (Capt. Kurrrk?); in a Borg dominated TOS, there is a command level drone that loosely inturpertes his directives (unit 5475...look at your cell phone); in a female dominated TOS, there is a devil may care Capt. with an eye for the lads (Capt. Jane Titiannia Kirk?) etc. Basicly, its like the idea that we all have a place in the universe. And it helps explain why the crews of various ships are together in the MU!
I know it's not "scientific", and it can be a bit corny,but it does help if you need some kind of connection to your crew. I sorta expanded on Comic book Alternate realities and Sliders.
_________________
"Yes, it's the Apocalypse alright. I always thought I'd have a hand in it"
Professor Farnsworth