Multiple Title IX exempt group membership.
 

For members of the NIC, NPC and NPHC (all of which are Title IX exempt) are there other Title IX exempt groups that you would feel comfortable with a member of your group also belonging to?

The only examples I can think of might be Phi Mu Alpha Sinfonia (for men) and Sigma Alpha Iota (for women). Are there others?

Are there other pairs of organizations that fit this other than (possibly) Y and Sinfonia or Z and SAI?

This is as a general practice, not exclusive to the letter of the rules. Omega Psi Phi is not an NIC member, and as such I *guess* you could legally have someone who is a brother of both Omega Psi Phi and Sigma Nu.

I'm also excluding Honorary memberships here, so President Trump receiving honorary membership in both ZBT and AEPi isn't an example here.

Clarifying question:

Is it the character of an organization which makes it Title IX exempt, or is there a determination letter?

I never thought about that before now.

SAI received our exemption via a letter from the office of Civil Rights in 1981 because it was determined that, while we specialized in music, we were originally established to foster close relationships among women musicians; therefore, we were deemed a social organization. As long as our membership criteria was expanded to include women from any area of study and require completion of one only music course we remain Title IX exempt.

I'm not sure what new organizations that lean towards a speciality area but want to remain single sex would have to do.

Maybe some of the Christian GLOs that are not NIC, NPC, or NPHC? I know the Wikipedia page for Sigma_Phi_Lambda mentions that sisters are not forbidden from joining another GLO.

In that regards, the sororities are slightly more likely, since a Christian Fraternity of about the same age and size (30+ years, 30+ chapters) (Beta Upsilon Chi) was able to join the NIC.

Nope.

How are Sigma Nu's bylaws written that would exclude an Omega Psi Phi brother from joining? And would that also include a Sinfonia brother from joining?

(I picked Sigma Nu at random from the non-NPHC members of the NIC)

We don't allow dual membership in any general college fraternity. The term isn't defined, but as applied, I would say that it would apply to Omega Psi Phi, probably Sinfonia as well, but that'd be a closer question, and definitely not to a professional honorary fraternity.