To play a "real" game? none. But we've doubled up Comms with Science, and Comms with Engineering. Basically, you need a Helms, Weapons, and Science to have a half-decent game.
Can you play without Engineering or Comms? Sure. But it's just not that same. Doubling Science with Comms means you get the missions and comminques, and are constantly reminded to scan things. Doubling Engineering with Comms means you miss out on a lot of the "fine-tuning" that can make or break the higher level-gaming.
But, in either case, you get a full "Artemis Experience"
We ran with 4 players, and actually "tripled up" one station: Science, Comms, Captain
The Science and Comms stations are all about information flow, and the Captain is all about decisions. The two stations are the most probably to volunteer vital information, so having the decision-maker simply access that information directly streamlined things a lot.
It definitely required a player who was solid at multi-tasking and communication, but when it did work, it worked wonderfully.
Helms, Weapons, and Engineering are 3 roles which, when manned by dedicated constantly-working officers, come across as absolutely vital to ship's operations.
Comms and Science seem to be two stations that, if a little slips through the cracks, then the other stations can pick up the slack.
When I have played, we have only had a maximum of four players. Each time we have played it like this:
Player 1: Helm
Player 2: Weapons and Science
Player 3: Engineering
Player 4: Captain's map and Comms
Helm is a hands on enough station (especially if you are using a Joystick) and therefore the Helmsman has no other responsibilities to distract them when they should be flying the ship.
Weapons and Science have worked well together for us. Out of combat player 2 can scan the ships and get the frequencies of their shields. In combat, they can use this data and quickly formulate tactics for the battle. Depending on who operates the weapons, the captain may allow weapons the freedom to engage the enemy as they see fit (to a certain extent, the captain doesn't just sit back and do nothing!)
Engineering, when played most effectively, is a very demanding role. That's why we dedicate it to one player only. They have monitor power distribution, damage control and energy levels very closely. We have found that proper control of energy can greatly increase the efficiency of the ship.
Captain's map and Comms work well together. Personally, when I have played captain, I have managed to use Comms effectively to deploy other vessels in to areas I plan to head to, in defensive positions or in a safe area. You have to almost work as a fleet commander as well as the Captain. The only difficulty I found was dividing my attention.