How about doing some sort of activity and assigning members to a group? Instead of forcing them to speak with EVERYONE, you can put names in a hat or something and pull out groups of (insert number) at random so you get people interacting.
When I went to an IMPACT conference through Greek life/NIC, we were grouped with members of organizations that we didn't interact with on a regular basis and had a blast.
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*does side bends and sit-ups*
*doesn't lose butt*
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