There is nothing in Alpha Phi Omega's bylaws that would prevent it and in fact an Alpha Phi Omega chapter should *not* use membership in another organization as a determining factor.
Thread on APO/GSS dual membership at
http://www.greekchat.com/gcforums/sh...d.php?t=112927
The only Greek Letter Organizations that I have seen that care about Mutual membership are the Social Greeks (incl NPHC) , somehow the Music Fraternities/Sororities and a *few* honoraries where they are in the same subject as each other.
As far as I know you could even have someone with membership in OPA/APO/GSS, but I think the most likely situation there would be belonging to one of the sororities as an undergrad and advising the other two as a professor.