Do you know of a detailed non-combat system

[Vladim]

I like The One Ring (1st edition, but most of the stuff applies to 2nd edition too). Classless, skill-based, dice-pool system with:

• detailed difficulties -> Check
• detailed modifiers -> Doesn't use modifiers
• detailed success outcomes -> 3 levels of success with (mostly) defined mechanical outcomes in combat, journeys and social conflicts
• detailed failure outcomes -> 2 levels of success with (mostly) defined mechanical outcomes in combat, journeys and social conflicts
• clear rulings about cooperation, retries, knowledge of success... -> some rules about cooperation, though a bit sparse...
• interesting special abilities or powers -> Check (PCs get culture-specific upgrades)

The system does not really address every possible action or outcome, but there are interesting suggestions about complications in journeys. These are called Hazards and they can be map-specific, as journeys are a big part of the game. Combat is too, and is decently detailed. On the other hand, climbing isn't, so it's one of those things you'd have to arbitrate somewhat with this game.