Product info pages are designed to stand alone, not be nested inside other info pages. This causes HTML/CSS errors, which might not interfere with your site's functioning, but are never good to have - they can interfere with search engines indexing your site, for one thing.
Validating your site shows 183 HTML errors. Most of these are relatively minor, but they add up, and many of them are caused by this nesting creating duplicate CSS id's.
The page you reference actually does not work correctly (or at least consistently); if you add the main product to the cart, it adds one of the first element instead (at least, after one element has already been added; I didn't add the main product first). Also, there is no indication of which items have been selected unless you go to look at the cart page.
Do you want the customer to choose extra elements beyond the multi set, or choose elements without necessarily buying the multi set? Various setups are possible depending on your organizational desires.
I think you would be better served by setting up attributes for the elements so they can be selected and deselected visibly before one "add" action puts them all in the cart. You can go back from the cart and edit selections if you want to.
If you want the multi set to be optional, put that in as an attribute and make the product "priced by attributes".