I would keep Pine because he has the highest Q score. The rest of the crew would have to leave for some unknown reason (maybe we could have guest spots) and is replaced all with guys that were in Kirk's frat from the Academy. They would go around looking for fun (we would blow up at least one planet per episode for the 'splosion quota)until Starfleet Command puts them on double secret probation.
While on probation, the Enterprise is followed around the galaxy by the USS Delta-C made up of sorority sisters from the Academy that had swaps with Kirk's frat. They would be uptight but hot and try to spoil the boy's fun. Eventually though, the crew of the Delta-C is so overcome by the irreverence of the crew of the Enterprise (and impressed with the number of planets that they've blown up) that they all have wild donkey sex on planet Orgy VII (cue lens flare).
Have a reboot each sweeps so we can change out the women actors and set up the tension of the guys melting them down to save money on writing. I've got two episodes laid out, one where a planet has turned into a utopia after they embraced fracking and another where switching to natural gas ends a war (good sponsorship opportunities).If the space thing gets tired we can have them all flunked back to the Academy where they have to get jobs in San Francisco while going back to school and keeping up their tans.