You can build your own cart functionality and then use cart upload to transmit the result to PayPal for checkout.
(Or better yet, if you can write API calls, use the Express Checkout API -- with SOLUTIONTYPE=Sole in the initial SetExpressCheckout call if PayPal is your only method of taking payments)
Basically, you have to build this sort of custom cart functionality yourself. PayPal will gladly process the payment with the information you then send, and that is all.