Vampire the Masquerade: Bloodlines had an ambitious speech system where different skills opened up different options and ways to compete quests, and also a degradation in speech options tied to the humanity stat (if you killed more, you became more of a monster). The benefit of that system is that you could bully people, seduce people, or mesmerize people depending on which skills you selected, and not every skill was useful for each conversation. I think that comes close to what are you hoping to have for quests (i.e. one high skill does not give you all options).
Of course, the downside of VtM:Bloodlines was that the end game was all combat, which rendered your social character less effective than a murder-bot.