Im guessing by "non-bglos" you might mean NPC organizations/NIC organizations... correct?
If so, many sisters in the DO chapter were also in Phi Sigma Sigma. Both organizations worked to schedule so that the sisters could attend the majority of events for each organization. It was not a problem. It was great publicity for Phi Sig as well!
We had some mister sisters who are also Phi Mu Alpha brothers as well... which on our campus - PMA was just like the other social fraternities
We have also had SAI sisters and I think currently DO has a sister who is in TBS, SAI and Phi Sig... dedication!