| The garnishment must first be satisfied before it can be "stopped" as you put it OR You can essentially stop it though if you change your job. Doing this does not eliminate the original amount of money you owe, it just makes that particular one halt in its tracks.
Then the attorney will have to figure out just where you are now employed and start the whole process all over again with your new employer. If you move to a different state or city, and work for a different company, that really slows them down considerably as they have to track you down. The attorney must find out who you are employed with (and in what state) and the garnishment can be started all over again against your salary from the new company.
And yes, you can be garnished by many attorneys at the same time provided that they represent different entities demanding money from you in different cases.
This scenerio basically turns into a case of hide and seek and once they've found you - tag you're it until you decide to go hide. | 
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