In New Vegas you had four basic options as to who you fight for: Mr. House, the NCR, the Legion, and the surprising option of Yes Man. Who at first seems to be the most logical choice, though then the idea of giving complete control of New Vegas to a robot who will dutifully take up the mission of any who ask starts to sound... not so great. I actually thought about this as I was rallying the various factions around "me", but I expected a mission to reprogram him or destroy, especially since my character had all that intelligence... Whatever...
Moving on, there will of course be different factions to put your faith in, but what if I want to make my own? There have been various other fine folk discussing this, but I want to take it a bit deeper. It has been made known you can build your own settlements, and there apparently many plots where you can stake your claim and where you can run your own caravans between them. It is also made clear that their are going to be people helping you guard these settlements and these caravans. It would eventually get old, having to be on the defensive constantly. We need to round up the posse and go smoke these losers!
You do that enough, you'd probably get a reputation for being a leader of men and women alike. That you have the power to keep these settlements safe. So then your settlements grow. And your army will grow with it. The problem with this, is the statement that the settlement feature is optional puts a kink into that theory. But what if we were to say that it is simply and instrument to grow and get different missions? It brings to mind Assassins Creed III where you had a homestead, but the ability to grow it was optional. I hope this is the case, but if not, the faction theory can still stand on its own, but it doesn't make much sense to have this freedom without the ability to apply your settlements to benefit your faction.
This would also tie into the rest of the world. Make the Brotherhood of Steel mad, expect an armored division at your doorstep. Even without a independent faction this would be a clever idea (perhaps not for the Brotherhood depending on the motives of this particular branch). This would also appease those who keep saying that Bethesda is limiting player freedom. I would love to conquer the waste. Or perhaps we do it through peaceful methods? Perhaps you use charm and charisma to convince (or force) raiders to fight for you? Thats a bit of a stretch, admittedly, but would be pretty cool. Imagine as well, standing on the steps of MiT as your loyal soldiers storm its doors firing round upon round at poor synthetic androids. Or it happens in reverse as you control an army that destroys the Brotherhood of Steel and claims Diamond City and all the rest for yourself, seeing as MiT could apparently care less about the outside world (though that is bound to change one day).
Now on to companions. You could make each companion an integral apart for various boost perhaps? A super mutant may make for an excellent bodyguard for yourself. A tech aficionado may give you turret boost for your settlements while he/she is not in your company, and when they are following you, you lose this boost. Or maybe you find a Cassidy-like caravan expert makes your more money while they are at home and once again with you they lose this effect.
There could also be perks that effect your abilities to lead and the attractiveness of your settlements. SPECIAL could also play a part in this. More Charisma = obvious effect. more Perception = the ability to weed out bad apples or an increased ability to see attacks coming, and so and so forth. Some perks could also influence your ability to communicate with outside factions. "Friend of Steel" perk may open up different options for the BoS (or higher intelligence could may them like you more) and "Wasteland Warrior" may perhaps give you more influence over raiders or other unsavory characters (strength could effect this). The possibilities are endless and the ways to approach how you shape your faction and other faction should be just as much so.