HI StoneDKr32 ,
Thank you very much for your question.
ATUM with installed premium version of Product Levels has this option, yes. You are simply talking about Bill Of Materials, right?
You can setup your handles as a "product part", so it is not visible to buy on its own. After that you add this product part into a sellable product A with the value "1" for example. That means when you sell one product A, ATUM will tell woocommerce to deduct 1 unit of handles from the stock. You can then connect like this the product part of handles into any sellable product. The inventory of handles will deduct from one place every time sale is made.
If this is what you need, pls read carefully all the documentation here and make sure there is no feature missing before you purchase.
Hope this helps.
Pavel