Yes, I'd say start with the smaller sororities - don't make the same mistake they're making.
One thing I found: Fraternities we wouldn't normally mix with, we were willing to do some sort of philanthropy event together. (I'm talking a one-day project, not an annual flagship event.) That can get the ball rolling to do more social mixers later on.
Plus, make 'em have a debt in your chapter's favor so they owe you a mixer! Send them flowers on their founders day (their flower, of course). Go serenading, assuming you can sing. Be one of the chapters that sends nice cards at Christmas, cards congratulating their new members, etc. It's kind of like a positive guilt trip.
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Alpha Xi Delta
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