In an ideal situation, there would be a multiplayer mode. However, for the multiplayer mode to make sense, it might even have to be an MMO, and that's just out of question. It probably wouldn't require enough interaction between players for it to make sense to be an MMO, but on the other hand in a galaxy so large, randomly running into other players would probably be too unlikely if there weren't as many players as in an MMO. I guess it might be able to get around this problem by using something like in Dark Souls though.
And then there's the issue where players are often jerks, so running into other players would be quite problematic in a game where you basically lose everything if you die. That's not so bad if the game is designed around dying, but I get the impression that No Man's Sky isn't such game. Sure, you can keep playing if you get defeated, but defeat sounds like an exceptional state instead of something that's expected to happen again and again.
Personally I don't think adding multiplayer support would be worth the huge effort. It's just so easy to get it wrong in a game like No Man's Sky. If the devs have an idea about how to get it to work, then by all means, I'm fine with it, but as it is, I actually don't even want multiplayer in this game. It'd be relatively easy to add something like a combat multiplayer mode, but in a game about exploration, that makes very little sense and would feel tacked on just for the sake of multiplayer.











