When you register a credit card with a new program, it is automatically removed from the program with which it was previously registered. You get two email confirmation notifications: one from the program that gained the card and one from the program that lost the card. You could actually use just one credit card for all of your dining programs so long as you remember to register the card for the dining program that should get credit for that day's meal. That's helpful when you're trying to meet a minimum spend requirement for one specific credit card.
So, no, you won't be able to double (or triple) dip the restaurant programs.