According to the cashier training manual, the legal limit on the Visa/AmEx gift cards is five per day per person. Any more than that, the pos will stop you, and you are not to do separate transactions to get around it. But at my store, we require them to buy them on the same sale (if they want to split them up it's because they have stolen credit cards). This means they either won't be able to use them with any of the cards or won't buy as much.
Other than that, the only big ones I have on occasion are the Disney ones, and they are just using the REDCard to get the discount for their vacation (and may use their pharmacy rewards card as well). Those people actually seek me out to do the transaction because they know I'm fast because I know you only have to scan the authorization barcode and move on to the next gift card....so I have them in and out in a quarter of the time it would take the other cashiers to do it.