Here's an idea of what I think would make a good social mechanic addition to 5e:
Wants and Needs
When you've got a recurring NPC, one helpful dimension to define for them are their wants and their needs.
An NPC's wants define their current goals and what they're actively pursuing. NPC's are usually pretty vocal about their wants, and don't hide this intel from others in normal circumstances. An NPC's wants could be anything they hope to achieve - an orc warlord who wants to crush the kingdom, a king who wants to raise an army, a barkeep who wants coin, a dog who wants a belly-rub, a polymorphed dragon who is looking for some adventurers to retrieve a lost scepter from her hoard. You can define an NPC's wants as specific or as broad as you like, but defining it - writing it down next to their stat block, for instance - can help guide the actions they take.
An NPC's needs define some deeper trait that explores why they're pursuing what they're pursuing. NPC's are often less open about their wants, and might not even be consciously aware of them. They are typically related to feelings and relationships the NPC might have. Example NPC needs include an orc warlord who needs to be seen as a champion of his people, a king who needs to feel like a true leader in the eyes of a judgmental advisor, a barkeep who needs to pay the hefty taxes on her establishment, a dog who needs companionship, or a polymorphed dragon who needs to feel safe. Similar to a want, these can be broad or specific, but the definition can help you judge when the NPC might change their mind about a want. For instance, maybe you can broker peace between the orc warlord and the king by convincing both of them to forge a peace that will last through the ages, increasing the power of both of their peoples and getting bards to sing their legends for generations.
Because needs are often hidden and powerful ways to influence an NPC, player characters aren't usually aware of them on simple interaction. It takes some effort to discover an NPC's needs. Usually, this means asking some questions about the NPC's life or about what they value. An NPC who is actively hiding their needs might require the party to make a group Wisdom (Insight) check to discover them, opposed by that NPC's Charisma (Deception) check.
Once a PC knows an NPC's need, they can use that info to craft a more persuasive argument. If the party is rolling a Charisma check to persuade the NPC of some course of action, invoking that NPC's need could grant advantage on the check.