If we're going to do this, we'll need to decide on a premise. We can have our ship captains attend some sort of conference, or to hew a little closer to the standard Trek format, we could all select ranks and positions on the bridge crew of a shared starship. I'm partial to the latter scenario, because it's a lot less formal and it gives us an instant excuse to do pick-up sessions whenever we want.
We also might want to consider designating a GM who can pose external events and answer questions like "what do I see if I scan for life forms?" I don't think it would turn into enough of a task to prevent also participating as a character, but I would be hesitant to take the reins myself, because I'm not as fluent in the lore as many here.