Can you build queries to populate category indicies?

I’m working on a Home Decor/Furnishing store that has around 10,000 products. We hav it all in Woocommerce – so the products are a custom post type “Products”.

The categorization has been a nightmare… the orignal developer did it by “manufacturer”… so, we have categories like “Furniture” and instead of having “Sofas” and “Beds” as subcategories, the subs are manufacturer names and then a third level of subcategories for “Sofas” and “Beds”.

The result is hundreds of categories and a not-so-great user experience.

I’ve mapped out an IDEAL situation, but I don’t even know if it is possible… could anyone help point me in the right direction? Here’s what I’d like to be able to do…

Narrow down the categories to something like:

Style
– Modern
– Country
– Coastal
– Traditional

Room
– Living
– Dining
– Kitchen

Item
– Beds
– Sofas
– Chairs

Collections
– Manufacturer 1 Collection
– Manufacturer 2 Collection

Each product would then be marked with all appropriate categories. So a sofa from our Baltus Collection would be in Item-Sofas, Collections-Baltus, Room-Living, Style-Modern.

On the front end, I’d then need to be able to have pages dynamically pull products that are in multiple categories… but only if the product is in category 1 AND category 2 AND…

So, if a shopper comes and clicks on “Shop Living Rooms”, they’ll see a category index for each top level category that has products marked “Room-Living”:

– Items – this will show an icon for each “item” subcategory that is also marked as “Room-Living” (and only those). So, it would be things like Items-Sofas, Items-Occasional Tables, Items-Ottomans. But would NOT include Items-Beds, Items-Desks, etc.
– Collections – same as above… just the collections that have products marked Room-Living
– Styles – again… same as above these would only show the Styles and only the “Room-Living” products would appear.

Is there a way to do this? Can the system pull products this way? Should I be thinking about it using tags instead?

Any help you can offer would be great!