A strange godlike being who traveled from the delta quadrant to test the mercy of humanity brings the Tuvix flower with him and spreads it aboard the enterprise. Most of them are vacuumed up by ensigns but one makes it into the teleporter when Scotty and Spock are transporting. Creating Scock. The rest of the episode is about convincing this new live form to call himself Spotty
It's actually a follow up for TNG, but I think there is potential in a movie about Q getting bored and making a star ship to explore space in staffed entirely by weird variations of Picard clones.
It could be called Qink