You could also run it like Ars Magica. Everybody has a senior officer who does important intellectual stuff on the ship, a junior officer who goes on away missions, and a bunch of redshirted ensigns who fill out those away missions.

For example, one player might have one character who is the tactical bridge officer in charge of security and weapons and stuff. They also have a junior science officer who leads exploratory away missions to gather samples or take some readings or administer vaccinations to the colonists or whatever. Then an ensign in each of the colors of the rainbow: a marine private for when another player's Junior security officer leads a tactical patrol, an engineer's mate for when another player's Junior engineering officer leads a technical crew to repair or hack or build something, a fighter pilot for when the carrier is attacked and the captain orders the fighters to scramble, etc.