Aside from decorating products, is there a way to assign multiple categories to a product?

By default they are placed as children of ProductCategory page, which enforces a certain convention on products and cannot really be used as a way to add more than one category. This works fine for very simple sites, but if we want to be able to browse/filter by more than one category then we need a better way.

There is the https://github.com/sunnysideup/silverstripe-ecommerce_product_tags module, however commonly what is needed is the ability to assign an attribute type such as "Screen Size" or "Manufacturer" to a product, and then select or enter a value for that attribute, whereas my understanding of that modules is that you can simply assign a tag to a number of products, but they cannot have their own unique value related to that tag.
These could vary enough that we wouldn't want to hard code them into the Product class, but assign them when it is created. Similar to Product Variations, except that they only provide information about a product to differentiate it from other products rather than separate variations on the same product. Newegg.com is a great example of how this sort of thing would work, although way more powerful than what we would need.

Does such a module exist or is anyone working on something like this?