No multiplayer; the devs would rather have a polished single player experience than a half-baked single & multiplayer setup.
Starfarer will have an rpg-esq campaign layer, where you basically go about the sector, doing what you want; be it running an elite force of mercenaries, turning a serious profit smuggling weapons, running a large-scale mining operation, building an empire, or what have you. There's lots of things you will be able to do - those were merely a handful of examples. This won't be in until after version .35 however.
Currently missions are in (custom ones can also be modded in very easily as well: custom ships & weapons can also be modded in), and they showcase the real-time tactical/top-down space-shooter aspect of the game.
There will also be a custom battle option down the line as well.