@Harrison,

I could imagine storylines involving the Federation, the Empire, or the Thargoids.

The player out to assist a heir of the Emperor in some plan to increase his sphere of influence, going through various contacts and quests.

Or perhaps investigating some deal your 'grandfather' Commander Jameson had left unfinished, now his client is on your back and expects you to finish of the job, not taking repayment as compensation.
You would have to trace Jameson's trail, meet some of his contacts and visit a variety of worlds.

Now it gets a little Star Trek like; an encounter with mysterious superior lifeforms that inhabit Hyperspace of have relocated their civilization there.;