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Yeah you can, but you should probably take the help of a Immigration Lawyer. Lawyer is there to help you out obviously but anyone can try to do it on their own if they know what to do.
The whole thing about the new law is that your OLD Employer cannot do anything to cancel your petition as long as you can show proof of current employment or proof of Job Offer available to you , with obviously same requirements as you applied the GC under. Again go and talk to a Immigration lawyer without wasting time to find out answers on this forum. These forums are only meant for Information not legal advices, so you might not get the best answers.