E-commerce and shopping cart software

The company I work for has been using the same shopping cart software for the last seven years. It's worked well for us, but we're looking to redesign the website and thought while we were doing that, we'd also take a look at what's out there as an option for creating and hosting the site. Right now we're using Nexternal. We're looking for something that would perform similar functions, but might have more or better options for us. Currently, we run an online store, with tons of products, with wholesale and public pricing as well as specialty pricing. We have the ability to offer coupons and gift certificates, take credit cards and Paypal. Customers can review products as well as share orders and products on various social media platforms.

We're looking for options for platforms that can do all the things listed above and perhaps also include things like multiple location inventory.

Does anyone have any recommendations for companies I should investigate?