Dr. William:

I will graduate with my PhD degree next year spring. I know there is no H-1B number available at that time. Is it possible for me to change to O-1 status if I meet the qualification requirements?

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Answer: 

Yes, with your PhD degree, you may qualify to apply for O-1 status, when there is no H-1B number available and an U.S. employer wants to hire you. The O-1 status is distinguished from other employment related statuses in that it applies to more types of work than other areas. But the requirements of O-1 are much higher than that of H-1B. 

Also, O-1 status could be obtained by those in H-1B status who have exhausted the full-authorized stay of 6-year limit.