What about getting hailed by HQ and assigned a mission of top priority or just a mission as a favor to a friend from Starfleet/Klingon Command?
In the Series some episodes involved the ship not having anything pressing to do, then all the sudden someone gets a hail from Starfleet, or whatever (an old friend from Starfleet) and they take the call in their quarters or right there or whatever and find out there is a mission of urgency or a mission of request to go to whatever.
Where are these at for the game for both Fed and Klingon?
I'd like to be warping to my next destination and get hailed mid flight and asked to do a mission like in the series like I described above. That would add a little more flavor to the monotony of the dailies and DSE's.
Picard is walking through the cooridor with Troi and gets a page from the bridge that there is an incomming message from so-and-so. His eyebrow raises and he looks at Troi as if to say, "Wow I haven't heard from that person in a long time, I wonder what's up"
Then Picard asks for the call to be routed to his quarters or the ready room and we as the veiwer find out what the episode is going to be about.
That sort of thing...
I don't think it should be tied to how many current open missions you have, unless moving to a new mission would interrupt your current progress. But, maybe having it limit to only one random mission at a time, or just for fun, only two simultaneous (like you get two conflicting calls, and you have to get to the bottom of the mystery).
I know it's sounds complex but I don't think it is outside the reach of what can be added.
I posted a while back about random distress and having it be the way you get knocked out of a fight.
i.e. - when you lose a battle you don't just spawn, you have to escape pod the crew and sit adrift until a team member or a nearby friendly comes to rescue your pods and repair you enough for you to get back to a starbase for complete repairs or even tow you (actual use of tractor beams other than a weapon)