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This is a huge one for our facility too. We are running into lots of issues with this.

THIS! I'm glad I'm not the only one. As we expand this is going to become an even bigger issue. I can't believe this isn't talked about more.

We also would like to run a variety of different leagues, mainly partner leagues. It would be nice to be able to register and play together every week.

I agree with this as well. 

We have this same exact issue! It's very frustrating especially as a court reservation system, not having an efficient way to also reserve rentals doesn't make any sense to me. Seeing as we are expanding our facility, if this issue isn't corrected we may have to look elsewhere for our software system.