Permalink structure is a hierarchy, each level should be descendent of one another, be more specific i.e. shop.com/products/books/fiction/harry-potter
where every book is a product, fiction is a genre of books and Harry Potter belongs to fiction books.
So in your example product/manufacturer/brand/model
every brand should belong to a single manufacturer and every model to a single brand from that manufacturer. If that is the case, just use a single taxonomy – product category and create a hierarchy.
If one brand can relate to more than one manufacturer you need separate taxonomies and your permalink structure has to be different.
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