Since you have both groups on campus, shouldn't TBS be women only,and KKPsi be men only? I thought TBS/KKP went coed only if there was one chapter on campus. (Am I interpreting this correctly? I hear you saying that BOTH chapters have male and female members.)
I was in band my freshman year, and we had both chapters, segregated by gender. I did not join, although I think anyone in band could join either. The groups usually worked well together, and didn't seem to be 'competing' for members or anything else.
Other than that solution, I guess the question is WHY does the other group seem to want to compete? If each group carved out their own 'niche' or identity, would that help? You guys could work together to support the whole music program, but one group could really do service, etc for the band, and the other for the jazz band (or something like that). Why are people wanting to join KKPsi? What is different about them?
I might just be talking outta my butt because I haven't experienced this, these are just my random thoughts.