No, you can not stack discounts. I'm an AP holder, but every time we've gotten the dining plan I've had to give up my AP room discount and pay rack rates in order to get the dining plan. This is both when we've gotten the DDP free (Sept '05 and Sept '06) and when we've purchased it.
I also got the 40% off and the DDP for Thanksgiving of this year (2007). The code I used to get the 40% off required that you get the DDP. I didn't realize the DDP was considered a discount. I know when they have offered it free it was, but I didn't know that when you were paying for it, it was considered a discount.