I´m not sure whether this is what you asked for but here we go.
My RPG sessions nowdays are roughly 80% social interaction. I´m not sure to what extend I planned it so, but it ended that way and both me
and the players seem to prefer it so. There is very little social interaction rule mechanics in play also.
Firstly, the player characters of ours are not adventurers per se, but commoners in a medieval game world. If the player characters would be
classical adventurer types, their main focus would be in taking risks for the loot or whatever price looms ahead. Now that they are
commoners, there is less reasons for them to go about and risking their lives for they have farms, houses, businesses, wives and kids and so on.
The ties already can have some kind of impact on character behavior. Also, if a character is a merchant, the propability of social interaction is way higher
than for a character who is a guard at the keep. Thus, one method could be in restricting the characters to something other than "action man" types and showering them with responsibilities, whether that would be about sickly parent, pregnant wife, seat in a clan council or whatever.
Secondly, the way RPG gameplay very easily becomes is that the NPC´s and the game world are "not alive". What I mean by this is that the GM has a
challenge in making NPC´s proactive in seeking the attention of the player characters. Otherwise, the gameplay is like a computer game where by
the NPC´s are only alive if the players end up being at the same place at the same time. Sure, somebody might call this railroading, however there is
a difference in showering the player characters with plothooks and letting them choose which ones to latch on to. I utilize both. I force them to make certain decisions and others are their choosing and still, they can always choose HOW they resolve the situation, but they must do it NOW or SOON.
I´ll give an example. A player character might be an innkeeper. He might be approached by his wife because one of the kids has been bitten by a sewer rat and is now ill. His employee might state that they are low on drink or food items and need to acquire more. There might be some hobo, who has passed out on the doorway of the inn, all these force interaction based on the role and responsibility of the player character.
The character walks by a tavern, where by he meets his guild mate who asks for him to make a donation on behalf of the guild for the the widow and kids of deceased guild mate. At the marketplace, he might hear a gossip, which is a plothook which he can pursue if they want, it could be that there is a contest of sorts announced but the details are hazy enough so he has to ask around. He can witness somebody beating their dog by the streets and he can intervene or choose not to, another plothook. He goes to a apothecary to get some medicine for the kid and the shopkeeper tells that the character has not paid his medicine bill, which is untrue, but he has to clear things out. In the end the character might promise a pint of foamy drink for the apothecarist to smooth out the perceived problem and now the character has to be at a place x by the time y.
So what I basically do is that I constantly throw the players plothooks, time sensitive issues and problems via proactive NPC´s, and I always throw more at them than they can handle with their time, so they have to be diplomatic, they are always busy and when they fail to fix the roof of the neighbour in time , they have to resolve it. When the player characters are constantly busy and have to make decisions in a short amount of time, it forces social interaction on their part and the play is an intense experience, even when there is no combat or physical risk involved. This also forces the players to prioritize while knowing that when they bow to one direction, they are bending over to another direction.
EDIT: Another tip, if you want to utilize these. I personally was not accustomed to GM this kind of constant interaction which keeps the players on their toes non-stop. What I did was that I started out with one player and when I became more confortable in bombarding the single player, I took another one and so on. Basically scaling it up gradually. By utilizing these methods, I presume you can do it in any setting or rule system by ignoring the rules to large extend when it comes to social interaction and force the player´s hand with time constraint and responsibility. There is never a moment when I have to say "Sooo, what do you want to do", the players should be forced to be both reactive and proactive and at the same time.