Can subsites share the main site's product catalog?

I have a client who wants to create turnkey versions of her online store using MarketPress and Domain Mapping. Let's say the setup would work like this:
--Client's domain is myclient.com and we've set up an online store at myclient.com/store.
--A new subsite is created at clientsclient.myclient.com and mapped to clientsclient.com.

She wants the store at clientsclient.com/store to be identical to the store at myclient.com/store, with a portion of all sales from the subsite going to the main site. In addition, she wants any changes to the products for myclient.com/store to be automatically reflected in clientsclient.com/store. In theory, all other customizations (e.g., email notifications) would be controlled at the subsite level (e.g., individual store settings).

The goal is to allow the subsites to rebrand the main site's store under different domain names, without anyone having to maintain separate product catalogs.