Well, you have a very valid question and not sure how to answer it.
We have a hot-tub-a-thon and invite one Sorority to participate each year. It is for a local Charity and both get PR from it.
ASA across the street from us do a teeter-totter-thon and have a Fraternity help them.
While it is each of the main GLOs local Charity, both get good Pr from it. After all, it goes for a good cause from both!
Hoped this helped?