The dining plan isn't a "pay by the day" thing, it's an add-on to your hotel reservation so if you opt to purchase the dining plan, it has to be for ALL nights of the stay on your reservation.
One way that folks get around this is by booking multiple reservations over the course of the same vacation. So for example, if I'm going to Disney for 6 nights but I only want the dining plan for the first 3 nights, I would have to book one 3-night stay with the dining plan, and book a second 3 night stay without it. You *can* book both reservations at the same resort, and have them linked on your account, but it is absolutely possible that you would have to change rooms. Lots of people do this when they plan split stays (reservations at different resorts during the same vacation).
The trick with that is that your dining plan credits expire at midnight on check-out day from the reservation that has the dining plan - you can't "save" credits and use them later when you are on a reservation that doesn't have the dining plan attached.