I have done some testing with tenacity up vs tenacity down. It is possible to have both of these debuffs applied at the same time. What actually happens is that tenacity up will trump. All debuffs are resisted. Order of operation does not matter.
Is this WAI? I would have though that they would have a sum zero effect allowing debuffs to be landed as per normal tenacity-potency check. From the description of each one, it is not clear which should trump. I would have though that in each case we are adding/subtracting a large tenacity % e.g. 300% which would cancel out if both are present at the same time.
This is relevant as the tenacity down mechanic on dengar has a good potential to counter rex/yoda's tenacity up, currently which only dispels are effective against.
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tenacity up says "always resist negative status effects"
so when you have both of them, you have your minimum chance to resist
but your minimum happens to be 100% So TLDR- Tenacity up should trump.