I think it would be interesting to see a Trek RP where each player plays an entire starship, not just a member of the crew. You could approach it multiple ways.

Way 1: Gene Roddenberry's utopia is in tatters as the Federation is no more. The Klingons, Romulans, Borg, or someone else infiltrated Federation space undetected and toppled the Federation's top brass, effectively taking over the entire empire. The result, however, remains the same: the (many) Federation ships that were in deep space when the takeover happened now have no allegiance. Some defect to the new regime, but the rest have no place to call home. Now they must deal with deep space patrols trying to get them to surrender or kill them, space pirates, and other orphaned starships (aka players). The Captains must decide on a new five-year mission.

Way 2: A space anomoly (or was it Q?) destroys a bunch of starships' long range communicators. Now they can only communicate with other vessels/starbases within a close distance. The result? Anarchy! Some ships (from ALL races) revel in the freshly cut ties and go rogue, attacking other ships and starbases for supplies, while others attempt to keep peace via diplomacy and trading. But it's hard for everyone, with rogue ships, space pirates and high tensions everywhere. One wrong move and you're getting a starship's entire weapon arsenal sent your way. How will you steer your ship and crew?

Way 3: A classic PvE war between the Klingons, Romulans, and/or Borg. You control a Federation ship, and must work together with other (player) vessels to win your battles and survive another day.

So basically: gritty free-for-all (Federation only), gritty free-for-all (any race), or PvE space romp.