The word and concept of "Switch" could really play into a Star Trek Switch game: "Switch Trek."
Star Trek has a lot of variety of crew members good at different things all doing different things at the same time, similar to how Stardew has you doing different tasks (gardening, combat, relationship-building). From hand-to-hand combat, to exploring, to crafting, to flying the ship through asteroid fields, to negotiations with alien cultures, "switching" tasks using a planets rather crew of different (yet team & goal minded) characters would make for great gameplay. A Kirk-like character could be fighting a Kahn-like in an action-RPG battle, all while Spock is negotiating on the planet, while Bones is tending to someone with a virus of spores in med bay, etc. You'd have to do it all! It'd be cool to have all the task-switching be timed to a doomsday mechanic like Majora's Mask.
You have to navigate journal tasks to meet with certain alien species/people, mine certain ores, fight off enemies/bosses, fly to different places in spacecraft, and achieve certain tasks by switching between different characters on different parts of a planet before a doomsday planetary event occurs: a countdown to extinction! Include time travel like Majora, too. Switching teams/leaders a la Pikmin 3 comes to mind re: exploration. Just a few thoughts!
Good luck!