[math-fun] Double agents, triple agents, and quadruple agents

I'm not sure whether this is a math/logic question or a psychology question, but it seems to me to be at least partly a math question: I know there have been double agents (for example, Guy Burgess) and I know there have been triple agents (maybe Kim Philby, I read somewhere). Have there been quadruple agents? Would that make sense? If it doesn't make sense, is that be for human psychology reasons alone or for logical reasons, also? (I'm pretty sure there's no logical reason why there couldn't be.)