Multiple Product Variations

Hi Guys,

I'm looking at using Market Press for a project for a bake-at-home pizza store. I need multiple, non-exclusive variations for their products.

For example, they offer 12 varieties of pizza (cheese, sausage, pepperoni, etc). Each pie can also be ordered with a regular (+0) or whole wheat crust (+$2), regular (+0) or low-fat cheese (+2), and as a physical pick-up or as a gift certificate.

Is there any way to add these attributes into Market Press as additional variations? (A hack is okay)