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Set priority to permalinks

I have a problem with the permalinks and I don’t know where to take it from.
Let’s say i have this setup:

  1. page with the slug stack : site.com/stack
  2. a product with the base url stack : site.com/stack/product
  3. a taxonomy with the base url stack : site.com/stack/category

I get 404 on the product page (2) with this setup. If I change stack from the taxonomy (3) into something else, the product page works.

The taxonomy and post type product all have the has_archive set to false.

How do I "trick" WP into get it working?