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Is your fraternity small compared to the sororities (and the other fraternities they mix with)? It is hard for a 150-woman sorority to mix with a 50-man fraternity, for example. We used to address this by having dinner mixers with smaller fraternities, so it was only the in-house women, and it balanced out better.
Also, if you are trying to get on their schedule for the first time, you may just have to foot the whole bill. That won't be a big deal if you can have a BBQ at your house or something.
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