The base of the system is cribbed form this
Angry GM post. What I'm layering on to is a way to track favors in influence with individuals and factions. This is tied to downtime activities. In the DMG there are some basic rules for finding things and gaining favors as downtime activities, but they're bland and not well-tied to normal encounter level play,
What I want is some rules that will tie influence and reputation more directly to actual 3rd pillar play, specifically to give the PCs some handholds to plan 3rd pillar stuff. For example, if the PC knows they call in a favor from NPC x, and they know they have the reputation to to get past the guards in place Y, they have some actual resources with which to make a plan of action. Along the same lines, if the players know they need reputation X with faction Y to gain access to the Duke of Chutney, they have concrete ways to go out and make that happen. It sounds mechanical, but in practice there aren't many moving parts and it's easy to work into table talk without breaking character. I'm also working up some rules for an encounter type in between down time and full encounter to represent smaller jobs (if you think of it in terms of, say, Oceans 11 these are montage scenes). There's a book on DMs Guild that ports some rules from Blades in the Dark to 5e for just this purpose that I'm probably just going to adopt wholesale.
The other goal is to decouple skills from stats to an extent, and also make some provisions for non-skill monkey classes that will give them at least a limited ability to bring something to the table in social and non-combat play.