Could have an alternate reality mission. Joint mission including both ships.
I'm thinking, The Discovery and the Churchill (hopefully with it's Captain back if he would like to), are sent to investigate a wormhole.
While there, strange readings begin emanating and soon, two ships emerge through. They're copies of the two ships, but heavily damaged.
While there, we meet other versions of ourselves and spend a bit of time talking, seeing what's different in the two universes.
But, trouble strikes when they ask us to return with them. They claim it would provide a tactical advantage, but we are forced to refuse. Due to the refusal, the two alternate crews then sabotage our ships, taking various items to assist them. Phaser Coils, Torpedoes, all the important stuff.
They leave back through the rift and we are forced to follow them, to take back our items.
It would take a bit of multi-role playing on our part, but it would be good to see how people would play their characters differently.