Is it possible to use different debit cards to pay for different services such as 1 debit card for Internet, another for international calling, etc?
I don't think so especially if they are on one bill.
The only way I can think of is to initiate multiple manual payments, each with a different card and for the amount to be the amount for the services in question. Seems like a lot of extra work, though, and you obviously would not be able to get a receipt that the payment was for a specific service, if that is what you are looking for.
