Order By Put up Kind ThenBy Taxonomy

Assuming I’ve these customized publish sorts:

1. Product
2. Video
3. Article

And for Product (WooCommerce Product), now we have many Classes, one in all which known as "Parts".

I’ve this example the place I must kind my search question utilizing the next rule:

1. Product (that’s not Components), then
2. Product (Components), then
3. Video, then
4. Article

Which means if I search a key phrase, say "engine", Merchandise ought to come out first (with predominant merchandise popping out earlier than components). Then Video and Article ought to come later.

Is it potential to seize such a use case?

I’ve solved the problem with "Sort By Post Type", referring to this publish: Kind search outcomes by publish kind

What puzzles me is, how can we kind by Put up Kind after which by Taxonomy, however solely within the case if the post_type is Product.

Any thought?