Storytelling
Of course, "just playing" the game is fine, and I hope you enjoy it. But you may do a little bit more with it, I guess. You make this game a Story Game by using not only your dice, but your imagination and your creativity.
When you play Stardrifter, you can write an entry in your Captain's logbook along. Narrating your story as if you were the Commander of the Star Trek Enterprise, or something.
Week 223
Taking off from Sheldia to Marsengorh. Full load of Electronics in the Cargo Units. All systems are GO, although I'm a little bit anxious about the Weapon system. Hopefully, the Warp zones are safe in this area so I'm confident about this trip.
Each time you build a New World using the Galaxy Generator, describe it. Try to imagine the way it looks, how are the people living there. Does your character know someone on this Planet? Has (s)he been there before? What is your character going to do with fresh money in hands? Drink it? Enjoy life until the next mission?
Each time you're travelling and bad things happen, why don't you try to vividly describe what happened? Were you scared? Why did you decide to flee instead of fighting? How did you negociate with the Space Pirates? How did you get out of trouble?
Week 224
When I knew that the Pirates wouldn't want to keep me alive, I had to make a choice. Flee or fight. My brand new gun cannons needed to be live tested. I made an evasive zig-zag, and they didn't have time to react: a couple of seconds after that, their engines were severly damaged, and they were unable to chase me.
I sent them a last call before re-entering Hyperspace: "I told you... You should have accepted my offer".
Your imagination and creativity is the limit. Why not publishing these story bits on a weblog? make an ebook, share it with everyone? Don't be shy, don't be afraid. Since Stardrifter is under the terms of a very permissive Creative Commons License, you are already allowed to make this kind of derivative work.
Two players
Stardrifter is meant to be a solo game. But you can play it head-to-head if you like. You can chose one player to be the Stardrifter, and the other one to represent "the Universe", i.e. everything else: other traders, Events, Ennemies. The other player can generate Worlds, too. Then it's the first player's choice to act as necessary.
Why not Roleplaying scenes, from time to time? When you have to Negociate for merchandise, for example...