Yes, the priority is a global thing, it applies to every search instance and every search term.
Results with the same priority are sorted by relevance.
So based on your example, I would set the relevances of products for each brand as following:
SPX – 500
Waukesha – 450
APV – 400
Alfa Laval – 350
Graco – 300
Murzan – 250
So there is a 50 point gap between each brands. That 50 point reserve is useful if you want to place some products higher inside a brand. So if you want to push higher a Waukesha product, you can set it’s priority to 451, so it’s top of it’s brand, but the SPX products will still stay higher.
You can use of course bigger numbers with bigger gaps, it will still work.Best,
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