Adding input fields to products and/or checkbox variations

I'm setting up a catering menu through marketpress so that customers can order products online. I'm able to accomplish the majority of what I need to do by using variations of a given menu item. However, some of them, if using standard variations, would have 100+ items in the variations dropdown menu. I'd like to either have a text field where the customer can input their choices or have checkboxes for the customer to select their options.

For example:

The Working Lunch Plus is a choice between any sandwich (there are 10, some of which have bread options) and a choice of an additional side (there are 10 sides). This would be a massive amount of items in the dropdown. It would work better for it to have a text field to input choices or like I said above checkboxes to select the sandwhich and then the side and so forth.

Just curious if this was possible through marketpress.