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The crewman visa is one of the worst visas to have. If you overstay, you CANNOT get Residency in the U.S. unless you get it through Asylum or Cancellation of Removal or similar relief. This means that marrying a U.S. Citizen will not get you a green card and not even having U.S. Citizen children that petition for you will not get you a green card. So no, you cannot stay in the U.S. and work while on a C-1/D crewman status. I am truly sorry for the bad news.
If you have a high enough education and you apply from OUTSIDE of the U.S. (since you cannot change status while on a C-1/D as a crewman, you might be eligible for an H-1B visa. You need to get a job offer. The job offer must be for a company that is offering a position that is related to your degree and experience. The position must normally require a bachelor's degree or higher. The company must have a need for someone in that position and must have the resources to be able to pay you what is normally paid to someone in that position. Also, because they are used up for this year, you will need to apply on April 1, 2017 to start working on October 1, 2017 or later. The exception is if you apply for a cap-exempt job and those are at an institution of higher education or its affiliated or related nonprofit entities or a nonprofit research organization, or a government research organization. Those are not subject to this numerical cap.
Here is an official link to the H-1B:
If you do not have the high education but you are from a country that the U.S. allows to have it, you can try for an H-2B worker visa again, from outside of the U.S. since you cannot change status while on a C-1/D crewman status. For an H-2B worker visa, it is expensive and difficult to get because the employer would have to go through an expensive process called a Labor Certification where the position is advertised in the local media, the employer must receive all resumes and eliminate all candidates for valid reasons, not just because they have a job for you. This is to prove that you would not be taking a job away from a U.S. worker. Here is a link:
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