Any popular fictional universe has its fair share of fan fiction - where beloved characters might behave less like they're written and adhere more to personal head canon - and it's the sort of thing that there's no shortage of in Star Trek.
I'm dead serious. There are actually comic books and a novel that involve a Star Trek/X-Men crossover.
While Star Trek Timelines won't let you revel in a brawl between Wolverine and Worf, you will be able to play around with all sorts of alternate dimension and timeline stuff. If you want Locutus of Borg tending bar at Ten Forward, you can totally do that. If you want Captain Janeway to lead Bones and Sulu into battle, that can be arranged.
Of course this means you'll be gathering crew from all over the various Star Trek series. What's cool is that this isn't a typical card battler type thing like you might expect. Instead, when you take part in a mission there will be several branching paths that your team will follow depending on the outcome of each encounter or task. Characters are automatically matched to a task based on their stats and stills, and a random number roll (influenced even further by their skills) will determine the outcome. In a weird way it's kind of like a choose-your-own-adventure but without the choosing and more seeing what the outcome is.
There are some typical choose-your-own elements to it, however. Before and/or after some missions you might have a few dialog choices to pick from, and your approach to a given situation could have an effect on your future interactions. The game is really quite story-driven, with more of an emphasis on problem solving and talking things through over full on combat - which I'm totally okay with.
What's also pretty cool is that you'll be able to use all sorts of different recognizable ships, each of which can give your crew different passive stat bonuses. You can also assign different crew members to different room positions, which might increase those bonuses even further.
Star Trek Timelines will be coming out later this year as a free download, and will most likely use a F2P system similar to Game of Thrones Ascent.