Father Tim, I usually run it with several separate but competing empires starting from the same planet, if you've read Steve's Trans-Newtonian campaign reports it is essentially like that.
I suppose there is nothing stopping a couple players, if they agree, from joint control of an empire though.
Vynadan, it is kinda abstract yeah, think of it as simply roleplaying without a set of rules in front of you. People can be as precise as they prefer.
The way I ran my last one is I provided the players with their starting resources, they would give me general or specific direction for how their faction would go forward and interact with other factions, then I would advance time for a while (exact time was not specified, could be a few months, sometimes a couple years) until something interesting happened, a goal was met, new designed ships were completed, an attack begun, or ruins discovered, things like that.
Once an event hit I stopped progression and did a report to the group of all the information that their factions would reasonable know, classified stuff would be reported to the individual via PM.
The players in turn would have private negotiations between each other, the results of which were reported to me. As well as public announcements and meetings which all could see. This allowed people to trade tech and resources, make and break alliances publicly or privately, and so on.
The level of detail in guidance is totally up to the player, you could present me with a list of tech research and goals and have me not deviate from it, or you could say something like "The Free Republic of Manila wishes to put a mean armed satellite into space as soon as possible, we are open to trade for the required technologies." And then just let me figure it out from there.
Though for trade I'd hope you guys could work out your own deals between each other, it was a part of the game my other players enjoyed.