My TOS went through a crazy shift where instead of losing the supply to my arm, which was my "normal" problem, the arm was instead turning purple and the veins were bulging huge. So I shifted from arterial compression to veinous compression. Maybe a result of changes due to PT or posture or who knows what.

Anyway in addition to moving the arm around like some of you have described above, I also got relief from shoving my first rib down. Here's how I do it:

I reach across with the opposite arm and place the pad of my thumb on where the rib would come up to the spine. Obviously there is muscle in between, but you get a feel for the position after playing around. Then I tilt my head 45 degrees to create some slack in the scalenes. Then I exhale while shoving down.

This would fix my purple arm.

I showed it to a relative. They thought it was freaky!

Anyway, just wanted to share that as something you can try. Good luck.