You may be interested in "Chimpanzee Politics", by Frans de Waals (something like that), which is about exactly that (observing a group of Chimps in a zoo, and how their politics and alliances evolves, with a couple coups).

But maybe we could. Considering the tricky setups scientists use to compare the intelligence of mice and rats I'd think that it should be possible to devise an experiment which teaches monkeys to reveal their clan structure. I'm thinking along the line of first training association of buttons with clan members (photos) and the allowing to select groups which should get or not get a treat.