your letters reversed...
 

Is there a group that contains your letters in the reversed order?
Is there any interaction /relationship between your group and that group?

(Obviously this question doesn't apply to Delta Delta Delta, Alpha Sigma Alpha and Alpha Kappa Alpha, etc.)

For Alpha Phi Omega, back when we were all male, a women's service sorority called Omega Phi Alpha was started in coordination with one of the chapters and this group eventually went National. No formal relationship with them, but we recognize that they are similar in most ways (so that of both exist in the same school, they are probably in the same council)...

(and I thought I asked this a while ago, but can't find it)

There is a Tau Sigma national honor society. I can't seem to find Tau Sigma Alpha.

www.tausigmanhs.org

There's a local called Sigma Alpha Tau

www.sigmaalphatau.weebly.com

There's a medical fraternity called Phi Beta Pi.

Pi Delta Alpha is International Honor Society for excellent students with disabilities.

I did a google search and came up with nothing. It just shows links for Sigma Gamma Rho :)

Took that as a challenge. :) I found
https://archive.org/details/oakyearb1977indi/page/146
https://archive.org/details/oakyearb1978indi/page/194

Don't think they are wanna-bes. :)

There’s Sigma Kappa and Kappa Sigma, but no relation between the two

Pretty much the only results I find for Iota Alpha Sigma are graduate chapters of a couple of NPHC organizations—that is, there isn’t an organization that is simply called IAS. Sounds like it would be a great name for a professional fraternity or honor society for International Affairs majors, though. :D

There is a Beta Phi Gamma local sorority at Lycoming College. I never heard of them until I searched the internet just now. Website: https://betaphigamma.wixsite.com/betaphigamma

Also, I found a reference to a Beta Phi Gamma that was a junior college journalism society. I'm not sure if it still exists.

Alpha Phi Alpha - palindromic
Omega Phi Alpha - already mentioned

Phi Xi Gamma - does not exist