Stacks on stacks on souls. AKA How do I break Stahlrim?

Now, I know that Fire Damage is buffed by Illusion and Destruction. Making Fire weapons ABSURD.

And, I know Frost Damage is ABSURD on Stahlrim weapons.

...Chaos Damage can do Fire AND Frost, AND Shock.

...Does it get the Stahlrim boost, as well as the DestoIllu cheese? Just one? Or neither?