Sorry for the quick reply - not sure if this helps (or is correct) but you could use the eCommerce/Product ‘categories’ as a more overarching/broader category.
Then using the normal CMS Collections you could setup ‘Shop Categories’ - which is where you’d input the ones you currently have.
Then, you could link the new ‘Shop Categories’ in the settings of the ‘Products’ under the eCommerce as a ‘multi-reference’ field, which would enable you to select multiple for each product.
You could then create the specific page (or use tabs) to sort your products by each of the new ‘Shop Categories’ and use the CMS Collections Pages to achieve this.
(i.e new ‘Shop Categories’ would appear down here and create specific link).
Hopefully makes sense.