Fiasco would work well. You can find a play set for it that is D&D themed that does a good job at creating an interesting starting party with lots of connections and needs.
While I think it always depends on the group-think of the table as to how murdur-y they get, in your case, I think The Caves of Chaos offer PLENTY of opportunities (if the group chooses) to role play through encounters... possibly convincing different groups to go at each other.
I think a case...