DCL will always be happy to take your money. Yes, you can pay more than the standard deposit. You will have to tell the onboard booking agent how much. If you don't mention it, they will just put through a charge for the minimum deposit.
GET UP TO A $1000 SHIPBOARD CREDIT AND AN EXCLUSIVE GIFT!
If you make your Disney Cruise Line reservation with Dreams Unlimited Travel you’ll receive these incredible shipboard credits to spend on your cruise!