The exercises that may help are going to be dependent upon the cause(s), however, I would think that there are probably similar deficiencies among the general population of people that suffer from this condition. Since I have vascular TOS, I will always have compression that affects my circulation. However, I have been able to greatly minimize symptoms.

For me neck stabilization exercises (specifically deep neck flexors) and exercises to address and reverse scapular winging have both been extremely helpful. As far as scapular winging is concerned strengthening my serratus anterior, rhomboids, and rotator cuff along with learning to not overuse my upper traps, pecs and anterior delts were extremely helpful. I would not suggest trying to go through this process on your own. You need an expert PT.

I have resigned to the fact that I will be doing deep neck flexor exercises almost every day for the rest of my life. If I take a couple days off from doing the exercises, I can tell.

Also, I have put and will continue to put A LOT of time into managing this condition. I spend 15 hours a week doing stretching, stability work, and strength training. I also spend about 5-10 hours a week doing cardio. Of course I was not spending this much time initially, it was a long process to get where I am, but the more time I put in the better I feel. If I spent 30 minutes a day doing exercises I'm fairly certain I would not be where I am today. It is definitely an uphill battle for a long time and requires dedication and diligence.