The first thing that bothered me about the factions is that they don't have much of a story to tell without the main quest line. This makes each gameplay unique because you can't play all the paths to victory in one playthrough but makes the factions a bit dull, other factions don't get any part to play at all. (Atom cats)
Therefore my request is that there should an extended questline for most factions outside of the main questline and a new questline for the atom cats.
My idea to extend the brotherhood storyline:
We know that the brotherhood has changed since the passing of the last Elder Lyons, back to its technology hoarding and backwards ways. What if some of the brotherhoods members don't agree with these policies of Maxson and want to revert back to the ways of Lyons. You could pick a side as member of the brotherhood and destroy or organize a revolution.
My idea to extend the minutemen storyline:
When the PC finds the minutemen they come across as the ultimate good guys, later you learn that they weren't all that good and brave in the past. In this questline you would huntdown former minutemen that went to the raider side. In the end you would set up a settler government with representatives from all across the settlements you have build. (Would require a certain amount of well developed settlements) With the PC ofcourse as head of state.
My idea to extend the Atom Cats storyline:
Right now you only have one quest for the Atom Cats, which would let you join them. But wouldn't it be cool if there was a whole rite of passage for them? Like finding an exclusive Elvis tape and broadcasting it across the commonwealth. Maybe even taking out the Gunners hideout in Quincy like they say sometimes as end quest.
Another idea I have is to create more unique raider factions with a unique storyline for each one of them, but I havent thought that out yet.