Other than state law? No, not really.
If he has "several" that he has been "using" than presumably he is taking them across the border in a "less than legal fashion" to use them in a free state like Oregon that is pro suppressor, or he takes them out into the woods or deep into private land for use in a "less than legal fashion".
Of course he could be filing for travel documentation for the suppressors and using them after that "approval" process were to take place, but one would assume he would have mentioned it as it's kind of a pain in the rear end.