Yes, if the cart developer has developed a 2Checkout module you may use a shopping cart with your 2Checkout account. More information on supported carts may be found here. Because our purchase routine acts as a cart, it is not required that you install a cart on your website in order to use 2Checkout.
We also have our own set of proprietary parameters if you wish to design a custom cart for your website. You may find more information on the supported parameter sets and the plug-n-play cart here.
If you are a cart developer and wish to create a 2Checkout.com. module, you may wish to contact integration@2checkout.com for assistance and certification that your cart is compatible with 2Checkout.com. If your cart has been certified we will be able to add the cart to the list of recommended carts.