No, but you can have multiple player controlled starships on the same server. With the full version, the communications station can request that starbases build new supplies and so forth, but the stations are still NPC controlled.
That being said, having a station “set” in which different crews could mingle, have briefings, plan etc… could work quite well. In most of the artemis games I’ve played, there’s been several space stations, so one way this could be done is to designate DS1 as fleet headquarters (with living space, briefing rooms, and so forth), whereas DS2,DS3, etc… are simple supply depots, and don’t have facilities for crews to disembark. This would also provide added motivation for the crews to defend DS1 (yes, npc starships can and will actively attack and destroy space stations).
Apparently, on the hard settings, the odds are seriously against the player crews (enemy ships get larger, more numerous, and may have unexpected technologies), so having multiple player starships working together would enable cool fleet tactics to help them punch above their weight.
It should also be noted that player starships can attack each other … which could tie in really well with RP … ship to ship comms, diplomacy, and combat (because the translator never quite translates “we come in peace” correctly …)
Another way to tie it in could be in the setting of a fleet training academy, where the simulators are IC simulators too! The shared space then becomes the classroom/ready room or somesuch.