Limit number of tickets to a group of performances

We're having a Family Pre-sale for our Academy Nutcracker and would like to limit the number of tickets a person can purchase to six across all four performances and two price types. I've looked at Offers, but that limits by price type and not across price types. I looked at Pricing Rules, but we're not really offering a discount during pre-sale so that didn't seem to work either. I also can't figure out a way to limit the total purchase to six tickets across the performances. All I've got right now is a Mode of Sale shift with a promo code that doesn't enforce the limits we want.

I'd love to hear if you've done something similar and how you accomplished it. Thanks!

Sara