I actually don't think there is any widely-known e-commerce software today that really centers on such Social capabilities (as opposed to implementing a few social features in plugins or extensions, like Facebook Like, Facebook stores, share buttons, etc.).
There's probably a huge market opportunity there, though. Maybe through co-browsing, maybe through something more akin to a social network for the merchants' customers.
Maybe something like a Quora for merchants?
Which shopping cart has true social capability?
Note that it should be pretty straightforward to implement OGP into any modern E-Commerce platform (Basically, it all boils down to adding a few meta tags to your page).
Because it's only about metadata at the page level (not at a more granular level), it's probably way simpler than implementing RDF or GoodRelations, for example.
Which E-Commerce shopping cart solutions have Open Graph Protocol integration?
If part of your strategy is to grow your business virally based on word-of-mouth, I would definitely recommend Magento, which has more "Social commerce"-related plugins (and a more vibrant developer community), like Facebook and Twitter integration on login, reviews and sharing, etc.
You can check out Magento's extensions directory and marketplace over at Magento Connect: http://www.magentocommerce.com/m…
Which shopping cart is better? Magento or Big Commerce?