As I understand it, the tuner moves the vibration wave of the barrel so that the muzzle moves the least. The weight is forward of the muzzle. I see no reason why a suppressor couldn't also serve the same purpose. Tuning it would involve a way of moving it forward and rearward to find the sweet spot. Most of the application of a tuner is in bench rest accuracy shooting. And I suppose long range shooting. The military sniper could make good use of a combination tuner/suppressor.

 

Using a muzzle tuner and a suppressor together is counter productive. As you use the suppressor
“with rimfire” the suppressor gains weight and will/does over a high count or long shooting session changes everthing. I see no practical advantage to the combination.

 

It looks like you can use an ATS tuner and a suppressor.

Adaptive Tuning System (ATS) - Competition Model (Tapered)

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Tackdriver2225 asked a question, I did the best I could to answer it. It is a rimfire group, but the question could be in reference to a sniper application or hunting application where only a very few shots would be involved. And you are probably correct in many cases there is no practical advantage, but being quiet is certainly an advantage in many situations. And if there is a benefit in the mind of the shooter, that can be enough to justify it.

 

Look into this companies rimfire suppressor, I was told the way you stack the baffles, it is a tuner also.

Asteroid Precision Rifles (aprsilencers.com)