At Bowling Green, Greek houses (all "official" houses are on campus and owned by the University) have House Directors. House Directors are usually (like 99.9% of the time) graduate students. Most are pursuing their Master in College Student Personnel. Occasionally two houses next to each other will share a H.D., but that's pretty rare. Or at least it was while I was there.
I've never heard of one being a member of the organization they are the H.D. for (conflict of interest), but most were greek when undergrads. During my time, we had House Directors who were members of AEPhi, ZTA, and ADPi.
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