Alternate universes?

I don't think this is such a novel idea, but I wanted to hear what other people had done or avoided doing in this respect. Now first thing: I am not talking about Mirror Universe! I am talking about playing Star Trek with the same rules, technology, organizations, etc that we are all familiar with. BUT changing out some major aspect, most likely rewriting a major part of history up to that point in the game or rewriting the status and interaction of the various factions. Some examples of what I mean could be:
* Keep Starfleet, the Klingons, and the Romulans, but dump the rest of the galaxy and go from scratch.
* For a more militaristic Star Trek, the Klingon (Romulan if you prefer) war never ended...or restarted.
* The main races are as we know them, but they aren't the greatest thing since sliced bread, like they are in the series. Instead there are far more powerful races in control and we are like the kids in the neighborhood (kind of a Babylon 5 approach, where there are Vorlons/Shadows/First Ones in control of most of the galaxy).
* The technology and cultures are the same as depicted, but exploration of the galaxy is radically different, either severely retarded (and the Federation is just starting to explore beyond a hundred light years around earth) or severely accellerated (the entire galaxy is explored and settled and it faces threats from other galaxies or we explore other galaxies).

I'm just chatting. Interested in what others have done. Hoping it might spark some discussion and spread ideas for other narrators.

Actually, I'm not sure my examples even are good for showing what I'm trying to describe. Basically taking a big piece of Trek, like the technology and/or Star Fleet, and putting them in a setting that is clearly not Trek. That's the extreme. The "barely changed it" version would be removing Klingons as the major adversary and replacing with your own, or any of the examples I gave before. I guess I don't have this thought through, which is why I'm soliciting others to describe how they made an alternate Trek. The essence is some complete change. Not just saying "everything up to episode/series X holds, then I'm making it up as I go" but saying "forget everything you know about X from the show, that isn't the way it is in my universe".