Yes! Any card you have registered to your account will earn rewards at participating merchants. Some merchants have limitations (for example, we may not see purchases made with American Express cards at some locations) that will be listed on the merchant detail screen. You can register as many cards as you like.
At this time you can earn progress with Visa, MasterCard, and American express. Some cards may not accrue progress (the card companies sometimes don't send us notifications for pre-paid cards, cards issued outside the US, etc). If that happens, just send us a snapshot of the receipt.