If this is low hanging fruit, go for it.
But if it’s already tricky and the support ticket use case us under serious exploration, I am not sure the category permission paradigm is the best place to start.
It may be worth exploring enhancements to the private messaging feature to enable these workflows.
The flexibility to add (or remove) additional recipients on either end was always something helpful for us when using any system for support tickets.
A few more thoughts here, but I could say more if that’s really the goal.