Collecting additional information during checkout - ecommerce

My organization is hosting a summer camp and we want to set up an online registration system where families can decide which classes they want to take, submit their registration info, and pay the registration fee online. Taking a look at the different modules available, it appears that the best option is to use the ecommerce module and add each class as a "product". This is relatively straightforward, but the problem arises during checkout. I need to capture additional information. For example, a family may have three people who wish to attend the summer camp. I need to find out the name of the person who is registering for each class and capture some additional information (such as meal preference, special needs, etc.). Is there any way to customize the checkout process to capture this information via a form?

Thanks!
Brad