Hi Kelly,
I am much more familiar with Volusion and 3Dcart, but I imagine that Big Commerce might work in a similar way. Inside the admin panel, when you are building products and categories, it is very easy to assign one product to multiple categories. As CleverPhd suggests, this is accomplished because the products aren't nested under category directories, they have their own.
Here is an example of one of the 3dcart stores I manage. This product: https://www.celebratecommunion.com/prefilled-communion-cups-with-wafers-box-of-500.html actually belongs to 3 different categories: "Prefilled Communion Cups" "Communion Supplies" "Home Page Specials" However, it retains the same URL across all categories. In both 3dcart and Volusion, when you are building a product you can customize the URL and then simply select with drop down boxes which categories you want that product to be applied to. I imagines Big Commerce would be quite similar, but having never used it I can't say for sure. As long as the URL for the product page doesn't change, you could put it in 100's of categories and it would never be considered duplicate content because it only has one unique URL.
I hope that helps a little. Let me know if my answer raises more questions than it answers 
Dana