Ask HN: Open source shopping carts with themes and multi-site?

Are there any open source shopping carts with themes and multi-site system where many carts for many different customers can co-exist each with a distinct look and inventory, similar to a WordPress multi-site install?

I do not want to build a shopping cart, but some of our customers want to sell auxiliary items along with their hotel stays like team t-shirts and stuff and I'm looking for an open source solution that I can extend to integrate it into our existing affiliate hotel booking engine as seamlessly as possible.

Basically I'm hoping to be able to have my booking engine add a hotel room to the cart, and then by extending the carts checkout process, and have it actually book the hotel through our API as part of the checkout.