I have one suggestion as of now that I think would be very neat, and I hope you will read on with an open mind.
As of the current state of the game, I'm not sure that there is a point in boarding any ships (or I might not know of one). Its fun to do, although if you are in the best ship since you decided to spawn in it, why claim the other ship...
This leads me to suggest that we can warp with the unclaimed ship, but to do so you must "Capture" it instead of "Claiming" it and leaving your old one behind. Right now it is possible to fly an unclaimed ship, although you cant warp with it. If we could jump to a station, we could sell the ship and make some credits. I still believe you should only claim one ship, although if you could fly your ship, and the unclaimed ship that you now control, and jump to a station to sell it, that would make it have a point in the game. This could pose problems, like a crew owning 2 ships and going around in them when that is not the intention. How you could get around this is adding a "Capture" button beneath the "Claim" button. If the ship is captured, then your ship wont try to shoot it, but you also wouldn't have the weapon capabilities of the captured ship. This causes you to have someone flying the capture ship with your team still on the Claimed ship protecting you. To add to the importance of selling the ship, your Chaos will increase significantly and other ships want to come and destroy you, and the vulnerable capture ship. Of course there are many ways you can make selling the ship quickly a priority so nobody attempts to own 2 ships, and this is just a suggestion that I think would improve the game a lot, and I hope you all will look into this with consideration and thought.
Also a quick note. If you guys add in multiplayer with many ships going around the galaxy, you could also allow the capture key, and this will cause the other players to be notified of a captured ship in the system, but will also cause the crew of the captured ship to restart as if they were blown up like it is in the current game.
Thanks for reading and thanks for providing us players with a fun, team oriented game!