How does the social interaction look like ?
Are things happening outside the battles, like in dungeon keeper where units train and sleep and if they do it effectively they ll be ready for combat when it occurs,
or is it more of a few extra settings while re-equiping the characters ?
(or are they happening through a story that's to be followed ?)
You could just give them all a single "directive" pre-battle, aka :Try not to get carried away in your rage/don't come into a fight or antagonize (character)/...
a character could also get so much support/cover from his team(because of their directives) that he can be given a directive to focus(boost) a combat-stat like accuracy.
What I've currently got sketched up is a network of faces, with red or green edges between them. If you click an edge, it might display a description: what are the strengths and weaknesses in this relationship. If you click a face, you can see the characters stats, equipment, history; and some little boolean personality traits. "Slow to forgive", "distrusts new recruits", "loves spicy foods". You'd probably have a way of spending influence to encourage friendship from this screen, or try to give/remove a trait.
The interactions themselves, I'm currently leaning towards random events. Characters announce they've begun dating, break into fist fights during training, have a wild night at the tavern and you're run out of town. I want them to be flavor heavy: a lot might have little in game impact, but help create a narrative to what's going on. You'd often be given options on how to handle the event, with different tradeoffs to each. Some would change your relationships with the factions who can give you contracts. The actual events would be triggered by various stats in the game. You'd also get notified if somebody has been performing better in training (leveled up) or stuff like that.
Combat I keep changing, but I'm currently picturing an animated brawl, with iconography to show how the battle is going. Arrows display who's fighting with who, little gauges show who's got the upper hand. Over to the side is text describing any particularly noteworthy events. This text would give a sense of how the social network is changing results: George shouts at Harry "What the hell? You're supposed to have my back". Sara and Dwight pull off a rehearsed routine and injure an opponent. He should be out for the battle. I'd color code those to convey when something that encourages bonding happens, and when they've gotten mad at each other. You could click commands on the side, or by clicking a mercenary, to change tactics. Different commands and tactics would be more/less appropriate based on the makeup of your army and their relationship. There would be occasional events in combat related to the network: characters would react to friends dying. If they happen to meet the killer of a friend in another battle, they might make some exclamation. Old friends suddenly on opposing sides might only lightly spar.
Outside of combat, you'd set the battle orders, possibly muliple formations. You'd have boxes for each position in battle, and would drag characters over. The boxes would change color depending on compatibility with the neighbors. I'm considering having two dimensions for compatability: opinion and trust. Even if two characters dislike each other, they could come to trust each other in combat. On the other hand, a veteran might really like this new rookie, but he's not putting his life in his hands too quickly. Characters would have different roles they excel at, in particular 1-on-1, 2-on-1, or 1-on-2 combat and whether they stand routed to the ground or dance about. This I picture as sort of like a very simplified Football Manager tactics screen. You'd usually only tweak tactics, filling in for an injured mercenary or pushing two apart who've gotten a little hot.
You'd sign a contract, deal with events on the way to the battle, view your opposition, maybe tweak your tactics, manage combat, deal with the outcome, possibly travel somewhere else, and repeat. The contracts themselves would tell stories, with a series of them chaining together to tell of wars, etc. The little random events would tell other stories about the lives of your men.