We did something like this for the new members the semester I pledged my local. A couple of weeks into the semester, we had a social for all the new members, their new member educators, and Panhel officers (I think chapter presidents were invited too).
The idea was for us to get to meet the Panhel officers and the new members of the other sororities on campus. It did backfire slightly - people tended to "clump" by sorority. I think you would need some sort of icebreaker activity that forces people to interact with members of other sororities whom they don't already know.
You could do the same thing with all the members; you'd just need a bigger room.
I'm not sure if this is quite what you had in mind... are you thinking of trying to address the issues directly, or just get people talking and interacting with members of other sororities in a social setting?