So, I'm running a Star Trek style campaign, and thus the starship the players will be playing on will require quite a few BP to capture that Enterprise feel. More than the level of 4 that the PCs are starting at are supposed to "have".
Any tips for adjustments to make to the game when the starship the players are playing on is a "higher level" than the PCs?
I'm doing this in one of my current campaigns. If you go a great deal beyond 3 tiers higher than the character's level, you can end up making DCs hard to reach for characters with level appropriate modifiers. Using the ship's tier for so many checks can make that a real drawback. Personally, I'd recommend not going much more than 2 tiers higher than player's level. Considering the Enterprise's lack of military capability, it wouldn't be too hard to pick up one of the larger frames and cut down on shields and weapons to reflect this start off.
I'd maybe recommend doing some handwaving with crew size, just to keep it a little easier to handle and go for something in the Huge size category. Put the crew into teams, and the ship also can no longer make planetfall, like the Enterprise. You may have to jury-rig a light version of a shuttle bay (as I can't recall if shuttle bays can fit onto a Huge frame). If you're looking at tier 6 or 7, it will be challenging to get everything on there, but that will just leave you with that bit of a feel when the Enterprise came up against dedicated (higher tier) military vessels.