Product Variant Multiplier

Is there a way to add a multiplying add-on to a product page? I want to charge $A for the base product, and $B and $C for optional add-ons, but right now I would only be able to do this by adding variants in every combination on the one product, which would just create a very long drop down of hundreds of combinations on the product page. I could also have the add-ons as separate products, but since they are less than the initial base product, I can't have the client purchase only an add-on without the base.

Additionally, if there's a code for the add-ons, can the quantity field also be hidden from both the product page and shopping cart? As changing the quantity would significantly overcharge the client.