Yes, absolutely, with the approved I-140 under your belt, the new employer can file a new H-1B petition on your behalf and request 3 years. Once you start work for the new employer, however, he should file a brand new PERM on your behalf, quickly followed by a new I-140 petition upon the PERM's approval. You will be able to reclaim and retain your old priority date under the first PERM.
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.
I agree with Giacomo. I am just concerned that you run to AVVO with these questions instead to the employer's immigration attorney. Giacomo is too kind so you got the answer. Most of us would simply tell you to discuss the matter with the attorney representing the employer and would have been completely correct in doing so. It is ironic that you did not even appreciate his answer and gave his the best answer mark.
The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter,not should it be viewed as establishing an attorney client relationship of any kind.
Although all this looks good ... I too am concerned that you are posting this question on an internet blog rather than speaking to the company's immigration attorney.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.