I've used something similar to this in the past, and am working on fleshing out a more complete system. Basically, going farther than not always using an associated ability score, skills don't
have an associated ability score and each skill can be used with each of the six attributes (in theory; some combinations won't be used often or at all), kind of like how Shadowrun has un-attribute-associated skills and always specifies "Roll [stat]+[skill]" for its checks. My skill list looks a lot like Corneel's, where each skill represents a general approach to doing things rather than representing the things you do.
Individual tasks/subskills for each skill (the "things you do" part) do have associated ability scores, though, based on what kind of task each is: Str-based rolls generally involved physical force or movement, Dex-based rolls generally involve finesse or complex/intricate/involved tasks, Con-based rolls generally involve long-term or endurance-based tasks, Int-based rolls generally involve knowing things (and replace Knowledge-type skills), Wis-based rolls generally involve intuition or observing/noticing details, and Cha-based rolls generally involve social interaction.
For a relevant social skills example, there are two skills for doing things in an underhanded fashion (Deception and Stealth, the former for tricking or misdirecting people and the latter for doing things unnoticed), and there's a skill called Culture that covers both "culture" as in customs and social institutions, like Corneel's Politics skill above, and also "culture" as in the arts and other upper-class pastimes. Here's how you might use those skills in practice and with which attributes:
Ability score |
Deception skill uses |
3e analogs |
Stealth skill uses |
3e analogs |
Culture skill uses |
3e analogs |
Str |
Fooling people as to what combat maneuver you're attempting, making people think you'll punch their head off if they don't cooperate |
Bluff (feinting), Intimidate |
Rapid stealthy movement, hanging from windowsills for a while |
Hide/Move Silently (with penalties for movement) |
N/A |
N/A |
Dex |
Legerdemain, pickpocketing |
Sleight of Hand, Open Lock (simple locks) |
Careful stealthy movement, silently removing windows |
Hide/Move Silently (used normally), Disable Device (traps), Open Lock (complex/puzzle locks) |
Playing instruments, art forms like painting or weaving |
Craft (Painting/Pottery/etc.), Perform (technical performance) |
Con |
N/A |
N/A |
Extended stealth (like a sniper lying in wait or hanging from the rafters to overhear a conversation) |
N/A |
N/A |
N/A |
Int |
Forging documents, making and using ciphers |
Forgery, Decipher Script (codes) |
Tailing people unnoticed, identifying hidden entrance points, constructing camouflage |
Knowledge (Architecture/Dungeoneering), Survival (urban tracking), some class features |
Cultural knowledge, navigating bureaucracy |
Appraise, Knowledge (History/Local/Nobility), Decipher Script (legalese) |
Wis |
"Reading" a mark for a later con, identifying fellow ne'er-do-wells |
Innuendo (3.0), Sense Motive (noticing lies) |
Noticing pressure plates and alarms |
Search, Trapfinding |
Identifying movers and shakers, determining how honest or corrupt an official is |
Innuendo (3.0), Sense Motive (getting a hunch) |
Cha |
Lying, making yourself look more dangerous or well-connected |
Bluff (lying), Intimidate, Gather Information (word on the street) |
Disguises, impersonation |
Disguise, Diplomacy (appeal to authority) |
Wheeling and dealing, public performance |
Diplomacy (illicit deals), Perform (emotional performance), Gather Information (gossip at a party) |
(A "N/A" doesn't mean those skill+attribute combinations can't be used, just that I couldn't think of a good example off the top of my head while making the table.)
So as you can see, these skill groupings mean that non-traditional social skills can all be used for social stuff, and there's some overlap in Bluff-like, Diplomacy-like, and Intimidate-like tasks depending on who the audience is and how you're going about the task. There's also ways to slice things up by attribute, like being able to train only certain attributes for a given skill for fewer resources than training the whole skill, having Bardic Knowledge effectively being able to substitute for any Int-based skill checks and Rage granting something similar for Str-based checks, and so forth, but that's all outside the skills themselves.
There aren't actual Bluff/Diplomacy/Intimidate skills in this setup that characters can take since all of those skills' uses fall under other skills (nor are there Knowledge or Spot/Listen skills, since those fall under Int- and Wis-based tasks, respectively, of other skills), but each of those is mostly covered by just one to three skills (Deception/Tactics, Culture/Empathy/Insight, and Deception/Empathy, respectively) so you can "be good at Bluff" without too much investment and it's possible to "be good at social skills" with enough skills trained.
So this has the benefits of the skill group/subskill setup I mentioned earlier, in that each skill covers quite a broad area so that characters can be fairly competent by default without investing too many resources into one area, but between splitting uses of certain old skills over multiple new skills and allowing training/specialization of subskills you don't have an issue where all the social characters invest in the same one to two "social interaction" skills and end up too similar to one another and you don't
have to make a character or creature good at a bunch of related things if you want them to be good at one particular thing.
And to your earlier point about magic skills, though it's not directly relevant to the social skill discussion, there's Arcana, Nature, and Religion for arcane, divine (druid-y), and divine (priestly) magic, respectively. They each have areas of mundane use--the usual Knowledge (Arcana/Nature/Religion) stuff, plus Arcana has alchemy, harvesting and using monster parts, and working with magic traps; Nature has Survival and Profession (Sailor) navigation stuff, the parts of animal breeding and training that don't fall under Empathy, and herbalism and potion-making; and Religion has the social religious stuff like holidays, minor miracles like prophetic dreams and omens, and everything related to undead-slaying. On the magical side, they all have basically identical uses for their different categories of magic: Str for busting through force effects or other magical barriers and disrupting usage of magical abilities, Dex for hiding somatic components or using them in constricted spaces, Con for concentration and not losing spells when attacked, Int for identifying spells and items and some parts of UMD, Wis for sensing magic, and Cha for the rest of UMD and misdirecting observers as to what you're trying to cast.
So not only does this slightly granulate the magic skills so that "magic guy," "sneaky guy," and "social guy" can all handle their main area of focus with a single skill if they want to but really need two or three skills to cover everything, but it folds together the directly magical skills with other skills that martial and skilled classes might find useful (fighters might want Arcana for mage-slaying and Nature for healing without a divine caster, rangers want Nature for getting along in the wild and Religion to deal with some favored enemies, and so on) so that at higher levels you don't have the noncasters who have been immersed in magic and magic-users for many levels now still being unable to ID an enemy spell because they can't afford to and have no pressing reason to invest in Spellcraft.