Yes, you can change and keep priority date. Unless you will go back to your current employer and they will support your I-485, then your new employer will need to file LC and I-140 for you if they are willing to.
Talk to your new employer's immigration attorney. They want you, correct. They should know the answer.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
The new employer can file a new H-1B on your behalf, and you will be approved for three more years, given that you already have an approved I-140. The new employer will have to restart a new PERM and I-140 process all over again, but you can preserve the priority date of your old PERM.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
The new employer may file a petition for you, if you are a valuable asset for them, also, their immigration visa attorney will provide all necessary assistance for you.
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