As a solo commander in control of a capital ship. You would perhaps have NPC or player officers under you. Helm, science, engineering, weapons, logistics and so forth...
Mission giver should be around too, meaning the fleet carrier could act as a mission hub.
You will not control the ship other by commands to your helmsman and other officers.
It could be more of a Star Trekkie experience.
In the message feed, you might get urgent mission updates or urgent events from your officers. Like "Captain, we are out of fuel soon! We need to gather new resources. Let me advice what system to visit for restock" accept/decline.
Of course you should be able to step into any of your private spacecraft of your fleet that are carried inside the fleet carrier and do solo missions related to this environment.
Also, players without ownership or access to a Fleet carrier of their own could get access by joining an NPC mission squadron with either protagonist Fleet carrier/carriers and/or antagonist target carrier/carriers.
This would open up for some galactic exploration missions with NCP fleet carrier/carriers as your hub. (Battlestar galactica!).
That is my two cents.