You can be in a GLO and a secret society (at Yale), a final club (at Harvard)*, or an eating club (at Princeton). This is also true, I'm told, of the secret societies at Penn and UVA. In fact, one often leads to the other. Both Presidents Bush were in DKE and in Skull & Bones (a secret society founded 1832) at Yale. Teddy Roosevelt was in DKE, the Hasty Pudding Club (founded 1770) and the Porcellian final club (founded 1791). But no, no double GLOs.
*In practice, I'm not sure if this is true nowadays of IFC chapters and the male final clubs at Harvard; it is definitely true of the NPC/NPHC chapters and female final clubs there. In fact, there has been substantial membership overlap between Theta and the "top" female final club. It may just be that male final club members today feel no need for IFC membership. I'm pretty sure that NPHC membership and a male final club are compatible.
An interesting side note: historically, the final club system was extremely discriminatory with regard to prep-school lineage and social standing, but surprisingly open-minded with regard to race. Even in Edwardian times, the handful of black students at the top prep schools could make it into a final club at Harvard. I don't know if this was true at Yale as well; my guess is yes. Princeton did not admit its first black undergraduate until 1946, so it's a moot question there.
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