SigEpLegacy,
Every day, I work with military students during the course of my professional employment at San Diego State University. In my experience, my vets have found positive and uplifting ways of connecting with one another, other students and the campus.
When he came to SDSU, one Marine vet felt he was lacking a connection with others who could identify with him. So, he took the initiative to form a campus club called the Student Veteran Organization (SVO). SVO is now going strong and makes a HUGE difference in the lives of our military students by offering camaraderie, support and service. They get prime billing at our campus Veterans Office and actually have a lot of clout. Do consider looking into forming this type of organization. More info here:
http://www.svosdsu.org/
SVO is so squared away that they just got approved to offer on-campus housing exclusively for veterans. They will be occupying a vacant fraternity house on SDSU's Fraternity Row. Check it out here:
http://www.sdsu.edu/veterans
So, yes,
it is possible to find those connections you are seeking without necessarily needing a fraternity specifically for veterans.
If that's not enough, as others have suggested, it is possible to join a [regular] fraternity outright. I currently advise a fraternity chapter - the president is a Marine!
I hope some of this helps!
.....Kelly