Hi Kris,
Thank you for giving me a clearer picture of the business model. Unfortunately, there is a serious lack of documentation as to a 'correct' use of Schema in this scenario. Presumably, you've already seen documents like these:
http://schema.org/LocalBusiness
http://schema.org/Restaurant
This is the only type of example I have seen of this, and while these documents identify elements you can use, they don't give directions for how you MUST use them.
To my mind, the branchof tag would be for something like a franchise - a fast food chain or bank or something like that which has a corporate headquarters and branch locations. Please understand, I'm saying this is just my reading of the definition of that tag, but I have a feeling every business experimenting with schema is coming up with their own definitions of what these things mean.
Before Schema, when I was doing everything in hCard, I would simply create a different hCard data set for each business in a multi-location situation. This was pretty simple, but Schema offers so many different attributes.
I'll ask the other moderators here if they can give any additional input. In the meantime, in case this helps, here is a very nice free schema generator tool I found out about a month or so ago:
http://schema-creator.org/
Please check back in. One of our other smart mods may have more to add to this subject.