Actually you can do almost all missions. The trick is to do missions with the less people first (to avoid the time penalties you get when you go to mission). Also the mission completion timer reset when you drag your second or third character to the mission, and you can use it to save some time while waiting for one of them to finish another mission. And last, since you get the penalties if the timer is out and nobody was assigned to the mission, better put one character from the wrong type than nobody.
But the multi-tasking idea is nice, I like it :D
PS : Obviously this is easier if you managed to recruit all NPCs and avoid losing them ^^