If you look way back in history, when all the fraternities were being founded, you'd see disbanded DKE's who started Sigma Chi and TKE's were an actual interest group of Phi Delta Theta that decided to start their own group when Phi Delt denied them. It is actually not uncommon to see an Alpha Delta Phi who was admitted membership into Sigma Chi or Phi Delt. That was, I wouldn't say pretty common, but it did happen back then...
Today, you'd see the national org. investigate each new member, and if they had membership in another GLO, they would not be allowed to join. That is, unless they keep it to themselves....
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