There's something I love about White Wolf's World of Darkness, this is something that had played a role in many games I participated in up to that point, but was something that had never been formally written into the rules. I'm talking about character backgrounds (not related to specific stereotypes of race) that provide some kind of mechanical interaction with the wider rules.
In a game like Vampire, you get backgrounds like "Status" (which define your position within your chosen society of the undead), "Generation" (which gives an indication of how pure the immortal blood is in your veins), "Wealth" (an indication of the money at your disposal), "Contacts" (assorted people who have knowledge and might be able to provide clues), "Allies" (the people you can call on when the excrement hits the fan), "Influence" (which reflects you ability to manipulate a particular industry to gain benefits), or "Mentor" (the relative strength and power of someone who has taken you under their wing).
In Werewolf, where status is measured differently and purity of supernatural blood is measured genetically, these two become "pure breed". Werewolves being more spiritual also gain access to a "Fetish" background (which determines the spirit bound items in their possession) and "Totem" (which is combined with other members of the group to create a guardian spirit for the pack).
Wraith uses these ideas too, but takes a very different perspective. "Wealth" means little to the restless dead, and the act of dying renders anything like "Generation" or "Purebreed" irrelevant. The version of "Wealth" used by Wraiths is measured in oboli, the currency of souls used by the dead, and Wraiths maintain a link to the mortal world through a "Haunt" (a place of significance in their life and a refuge in their death), "Memorium" (which reflects how many people remember them, and thus their metaphysical strength), and "Eidolon" (reflecting how strong the character's metaphysical will is).
All character get a base amount of points to link into the wider community. They may choose to spend these points in a way that ties them closely to a particular group, they may spend the points in a way that gives them friends or other communal benefits, or they may spend them in a way that will make them enemies. Regardless of how the points are spent, a competent Storyteller/GM will make use of every point expended and find some way to link it into the wider story.
This Vampire character has points in "Generation" and "Status", they obviously think of themselves as a bit of an elder and they want to play the political game. This other character has points in "Influence" and "Wealth", they obviously still have strong links to the mortal world, but since they didn't spend points in allies or contacts, they're obviously a mysterious shadowy figure who manipulates things from a distance. Beyond their specific individual statistics, these points tell us about the characters role in a community and the relationships that might have significance in their ongoing story.
I've played in a few games over the years where backgrounds were paramount, personal statistics were stripped back to simple figures drawn from the wider attribute categories (physical, mental, social) and simple ability switches (do you have the ability, yes/no?)...in fact the live action Minds Eye Theatre basically runs like this. I've played in games where the entirety of the game mechanics revolved around background points (sometimes rolling dice, sometimes straight comparisons of numbers).
I'm thinking of something similar for "System 4/Other Strangeness". Beyond the raw verbs you use in a given situation and the adverbs attached to them (which grant automatic successes), I'm thinking of using backgrounds or relations that might boost a characters capabilities. But such relationships are distinctly two edged swords, they are generally positive (adding an extra die that might generate additional successes), but they might also apply additional advantages/disadvantages to an action attempt where they are used, and they might require narrative elements engaged to refresh them. Here's where the feedback loop between character actions and wider community repercussions come into play.
Some of the backgrounds/relations I'm thinking of so far include...
Allies - close friends (this bonus reflects the people beyond the other PCs who can be called on when things get tough. Benefits might depend on the ally, and each ally should be detailed for something they're known to be good at and something that they just wont help with at all. When used, an ally might require service to be reciprocated before they're willing to help again.)
Contacts - loose information networks and sources (this bonus is used to get information about things that might not be directly in the character's sphere of influence. Benefits might add clues to an investigation, or indicate how or what is necessary to proceed. When used, the information might be wrong, or it might come with a price attached)
Equipment - this one's pretty obvious (this bonus indicates pieces of signature equipment that the character has practiced with. Benefits might include higher damage from weapons, better results from technical gear, or simply modified gear unlike anything that other people possess. When used, there is always the chance the the equipment might break, or it could get stolen)
Mentor - an elder or teacher (this bonus reflects the benefits that might be provided by someone with great experience, possibly teaching skills, imparting clues, or just helping out. Benefits might include training sessions or montages, healing, or using their status in the community. When used, the mentor might retract from the character so that they will learn independence, or they might even risk being neutralised by the character's enemies)
Sanctum - a place of refuge (this bonus may only be used when the character is in or near their chosen place of safety. Benefits reflect the character's knowledge of the area, how well stocked the sanctum might be, and how well concealed. When used, it might dwindle the stocks, or draw enemies near and compromise the location's safety)
Status - reputation among a group (this bonus only applies when dealing with this particular group, perhaps some corporation, gang, ninja clan, or mutant underground. Benefits reflect the deference that other members of the group might give the character, and the favours they'd be willing to give purely because of the character's position. When used, it might eat into the character's social capital, or perhaps the character might be expected to fulfill certain obligations to the group to maintain their status).
I'm sure there will be more ideas for these, but that's what I'm running with for the moment. I haven't even specifically come up with the way they'll be applied mechanically in play...I'm sure it will come.