Been a while since I posted but wanted to share a scenario from our most recent session that everyone seemed to enjoy that involved inter-party conflict, though in this case it was a social conflict.
The set-up for the scenario involves them searching through a cruise ship, in this case an updated sister ship of the Titanic called the Queen Anne, for the drummer maintaining the necromantic ritual that had brought a sunken naval destroyer to the surface along with its complement of now zombified crew who had been boarding the cruise ship and attacking everything in sight.
So they get to the No.5 Hold, defeat the Renfield's at the door, get inside and pinpoint the Drumming to a large pile of crates in the middle but as the begin to remove crates to get to the center one of the characters is mentally attacked by the unknown baddy they can't see yet who tries to dominate him into stopping the others from removing the crates and I tagged an aspect of his in addition and he accepted (Fate point whore!). Which lead into the Social Combat / Mexican standoff as he pointed his gun at one character and another character (an FBI agent who didn't like him to begin with) pointed his gun at him. This lead to several rounds of social challenges of deceit and intimidation or presence while he tried to convince them to stop, they were confused and trying to get him to stand down etc etc etc...and every round the baddy continued the domination until they finally defeated him (earning him bonus Fate Points for being "taken out") and the baddy switched to a new target.
The upshot is that Social or Mental Combat can prove to be just as challenging and fun as Physical Combat!
I think I read somewhere or was falsely told somewhere that characters couldn't run social or mental challenges against each other, but if you can shoot at each other, why not? The difficulty in this particular scenario is in having good enough role-players that won't act on out-of-game knowledge and fortunately my players are all excellent role-players so the scenario was a lot of fun! So don't be afraid to use social Combat to talk down a character that is about to do something stupid, sometimes failure can be rewarding!