The first way would be a pvp multiplayer mode. That means you would be in an open universe, together with many other players and bots (like an MMO), because fighting the same player again and again would be boring.
I wouldn't like that kind of mulitplayer. It would destroy the balance of the game: How does the game find ships with the same strength, What happens when you die? How does it manage pausing?
The enemies HAVE to be bots to make it enjoyable.
So the second option would be coop, either with multiple ships or together in one ship.
Having multiple ships results in the same problems: What happens when a player dies, how does pausing work?
Also, everything needs to be rebalanced again.
So the last option is: 2 (or more) players controlling the same ship. I think every player should have full control of the ship, and not be bound to a crew members.
That also means that players can enter or exit the game any time, because only one player (the host) is required to keep it going.
The game mechanics and balancing would be exactly the same with only minimal changes (like a separate key for pause and unpause, so when players hit PAUSE in the same moment, the game really stops

It's just important that there is a text and voice chat, so the players can always communicate and make the decisions, and that all shop screens and text boxes are visible for both players.
The last game i played that included this kind of coop mode was Age of Empires 2 (the best rts ever).
When you selected the same team color, you spawned in the same village, controlling the same player. One player could focus on the army and attacks while the other player did the farming -- Really cool.