The regular ticket phone number will not work, but if you are using Disney gift cards, they will give you a second phone number to call.
When I called the second number, I was told that three forms of payment are accepted per transaction. HOWEVER, an unlimited number of Disney gift cards can be used because they count as 1 payment method.
I bought two 5 day base tickets in one transaction and paid as follows:
Card 1: Disney Visa Rewards Card
Cards 2-6: Disney Gift Cards ($20, $20, $50, $50)
Card 7: $10 balance after all of the above was applied was paid with AmEx gift card