While there is no official or written rule on belonging to both an NPC and NPHC GLO, I would think that a woman would prefer to pledge her allegience to only a single organization - after all, it's a lifelong committment! And I imagine involving one's self in any given GLO's activities would be quite enough for any lifetime.
But that's just my opinion.
Here's what I've experienced. As always, my POV is that of a non-NPC and non-NPHC greek. My experience is of an up-&-coming national GLO on a very greek campus.
The act of establishing my sorority at my alma mater made my sorority a national entity, from a local. As far as the university is concerned, we are a student organization with the focus sisterhood among women in technical studies (since we are not affiliated with NPC, NPHC, or any other "umbrella" org).
The current NPC advisor at my alma mater was moved to comment that according to NPC rules and regs, any NPC woman could rush and join our sorority, however because of our rules, that wouldn't happen. (Her background is law, so I'm not surprised she commented on that technicality.
) There have been a few instances when a young lady already pledged or a member of an NPC sorority will enquire about our sorority, and then decline their interest after finding out that we don't initate women who are already committed to, or members of, another GLO.
Before my sorority was well-established on campus, there were many women of color who showed quite a bit of interest in my sorority, thinking that we were special-interest/honorary. Many were on the verge of pledging their candidacy, when they simply lost all interest, and were very tight-lipped about why. I was in charge of Rush at the time, and was baffled beyond imagining. (This was long before I educated myself on the nuances of
all greek like.
) Understanding began to dawn on equeen when I found nearly all of these women, several semesters later, sporting letters of NPHC and CNHL sororities.
Official rules and regulations aside, I suppose it comes down to how (a) a group defines its membership, and (b) how it perceives the membership of other sororities/fraternal organizations.