Given that it's been mentioned but not described, here's the Exalted system

For a non-magical social attack, you roll charisma/manipulation + Presence (to affect one person) or Performance (to affect a group). They defend subtracting an essentially prerolled pool (the appropriate pool halved) from the attackers successes – they either 'dodge' by ignoring the point made (based on Willpower and the Integrity skill), or 'parry' by arguing the point (Manipulation/Charisma + the appropriate skill – Presence/Performance as above in most cases, but alternatives are possible.

There are other factors, you can 'aim' by monolouging – speaking longer to make your point more telling, conceal your 'attacks' using Manipulation + Socialise, and so forth.

One important factor that adds depth to characters is how their personality makes them easier to persade of certain things, and harder of others – character's have intimacies, which are things that they care about. This can be anything from your protective love of your niece, to your love of eating fine food, your hatred of the Mask of Winters, or whatever. They also have virtues (compassion, conviction, valour and temperance), and a motivation (player's chosen long term goal for the character). Social attacks that align with your intimacies, your virtues or your motivation get steadily harder to resist (in that ascending order), whereas those that go against such, or are dangerous, are easier to resist.

A successful social attack can do one of two things. It can make you do a given action for a scene ("Wash the dishes, dear!") if it doesn't go against their motivation, or it can build or erode an intimacy. Doing the latter takes time, as it takes multiple scenes efforts to create or destroy an intimacy, but if well chosen it'll mean they'll be easier to persuade next time.

Now, one of the utterly critical parts of social combat is this: In the absence of supernatural effects, the negative results (forced action or intimacy change) of a social attack can be ignored by spending a single point of willpower. And you can't force someone to spend more than two points of willpower total in a given scene using natural mental attacks (no matter how many try – once they've spent the two, they're just not listening to anyone).

This means you can have the crowded bazaar of insistent merchants, or the enticing whore, present the "You know you shouldn't do this, but go on...", and make it an actual effort and cost for the character to ignore the wiles that they are less removed from than their player.

Given time and captivity, you can break someone. Given time and a neutral group, you can instill your values into people. But it steers well away from causing the issues of "You're playing my character for me".

Any non-magical social combat system should have similar limits on what people can be made to do through it, I'd say.