Unlike William & Mary undergraduates, who are admitted in an "undeclared" status, Joint Degree students are admitted to one of six academic programs:
You might be able to change your major in your first or second year in the program. Work with the advisor of your prospective major to see if it's possible for you. Making this sort of change can be difficult. The limiting factors are your course history (do you have the prerequisites that you need?) and space in the Programme's major.
You must make steady progress towards the degree in order to continue in the program. The Programme's Catalog Supplement details the major course requirements that you should complete each year in order to stay on track.
Due to the demands of the Programme, you will not be able to double-major. With proper planning, it may be possible for you to earn a minor at W&M.