Apprentice mate, 500/1600 mate, 100 ton master question

Thanks in advance to any responses.

I have almost always found an answer to my questions just by browsing through the forum here, except for this one. I am gathering my paper work together to apply for my first license. I qualify for all three stated above, however I do not want to sit through the steersman’s program. I know I can get the 500/1600 mate get my signed TOAR for western rivers and great lakes, both separate DE, and start riding as mate of towing. Can I at the same time start riding as Master 100 ton, once passed, and upgrade to the 500 master and then upgrade to the Master of towing. My main job is tugs, but there is lots of relief work for 100 ton Masters I know of is the reason why I ask. Once you get the mate of towing are you stuck with it until the four years is done?