I'm not sure if the FATE approach would fit with your oldschoolish system, however...
Imagine you've got a second set of hit points that are more of your mental hit points.
Then break things down into rough equivalencies:
Charisma = Strength
Intelligence = Dexterity
Constitution = Wisdom
I'll ignore Willpower and Speed for the sake of the example.
So you have a social encounter where what is at stake isn't each party trying to kill each other, but instead whether or not a debate, argument or other social conflict is trying to determine who "wins."
Rather than in d20 when you would have a diplomacy roll that would resolve the whole situation, instead you'd lay out a detailed social combat system with various ways of attack the other party's position. Intelligence would in general be your to hit bonus, Charisma is your damage bonus, and Wisdom would explain how many social hit points you have.
The whole system would be intended for those people who want to game out what traditionally is a roleplaying moment. Instead of trying to convince the Emperor that his smooth talking Vizier is corrupt and plotting his downfall through normal roleplay conversations, relying on player skill to talk their way through things, instead you'd have the conversation play out like a combat encounter. Who ever gets their social hit points whittled down first would end up losing the argument.
The problem with social conflict is that the equivalencies work up to a point, but then the analogy to physical combat starts to fall apart. There might be solutions to that, but it would require a lot more brainstorming and vetting out details and subsystems.