Hey Greg,
If that's happening post step 4 i.e. Completed shopping cart is brought back to Ariba, the end user can directly choose to delete the specific item(s) from his PR(Requisition or Purchase Request). In order to communicate this back to the supplier site, you might have to check if you customize a submit hook/trigger. This would be an easy customization if you are using an on-prim solution. If your Ariba implementation is on the cloud or on-demand, it should be easier to change the logic to allow Quantity 0.
Regards
Vilas