A Limited Liability Company ('LLC') makes sense in your situation. The facts you present warrant working with a sophisticated Business Law attorney to make sure you get it right (legally and financially) the first time. See Avvo.com under Find-A-Lawyer. Good Luck on your Business!!
I agree with my colleagues on this, yes it can be done and even yes it can be profitable. You can do a similar thing with trade names and telephone numbers. I know of someone who is doing this very successfully with residential plumbers.
Before you do this, though, you need to hire a local lawyer who practices in business and franchising to give you guideance and get it done right the first time. Do it incorrectly and you will be paying for years.
For the older ones of us here, it is like the old Fram Oil Filter commercial, "you can pay me now or you can pay me (much more) later." As Michael suggest, check Avvo for a good reference.