Can I have multiple sites that each have the same store?

This is a network marketing model, so each company distributor would have her own unique website at say, 459596.mycompany.com that would be her unique website. The site would be primarily for product sales, so we'd use Marketpress and a shopping theme.

The question is can each rep have their own "site" but have the products in the store controlled from one place. In other words, we don't want the reps to control the products in the store.