Hi again! Julia,
Unfortunately, you cannot purchase the Dining Plan without having the Magic Your Way Package. These do go "hand in hand". Also, everyone in your room must also be on exactly the same package, for example, you are on the Magic Your Way Plus Dining and then the others who are staying in the same room must also be on this same package.
Here is Walt Disney World's own wording from their website for the terms and conditions of the package details:
The Disney Dining Plan cannot be purchased separately. It is one component of the following
Magic Your Way packages: Magic Your Way Package Plus Dining; Magic Your Way Package Plus Deluxe Dining; Magic Your Way Premium Package; Magic Your Way Platinum Package. To enjoy the Disney Dining Plan, you must purchase one of these packages
prior to your arrival. These packages are not available for purchase after your arrival.
Have a look at this
link for more information on these packages and what's included! Enjoy.
Brigitta