I think it was on this board I heard about reversing the positive and negative modifiers for Soc in some circumstances. And if not here, ... some other Traveller board. Trying to Persuade a belter or a planetside, low tech scavenger of something, nobles roll at a minus, low Soc characters roll at a plus. Admittedly an outside the book solution, but I thought not too uncommon given it's not mine.
Then another partial workaround is for the GM to mix up what stats you call for with what rolls. Intimidation might be Persuade + Str, while getting a favor from a Belter might be Persuade + End (from him sizing you up for what he respects, not literally badgering him forever). This is arguably RAW (under
Which Characteristic? in Skills and Tasks), but they don't quite spell it out to the fullest so it's easy to default to the listed stats for skills. The limitation to this one is it takes some GM fiat or players just think up some reason their best stat always applies to everything, but it's still a thing I've used infrequently.
After wrestling with it myself, I've rationalized Soc as not simply social standing as we understand it today, but a mix of caste, command presence, and honor/trustworthiness in almost a Pendragon stat sense. So a 12 Soc character gets his bonus in most circumstances not so much because belters find him likable personally as because even the 2 Soc belter can assume he always pays his debts, or he'd no longer be Soc 12. (And, in my game, break enough big promises and that becomes true.)
I introduced secondary characteristics because they were constantly needed when running games.
Perception, determination and influence are the three I decided upon.
Rolled or derived?