I need customers to be able to switch on/off products to buy within their "My Cart" listing page (By default Magento let customers only remove items from the cart).
Is there a method or an extension to achieve this result? I'am attaching a picture as an example of what I need.
I am not sure, however you can try Wishlists for Magento, such as http://docs.magento.com/m1/ce/user_guide/marketing/wishlist.html
A wishlist is a list of products that registered customers can share with friends or transfer to their shopping carts at a later date
Hey there, unfortunately no. That's something I gave up searching for. The one you mentioned for Magento 2 seems to have nice features.