Yes, in theory you can have two different application pending.
Talk to the immigration lawyer(s) working with both of these companies ... they need to be fully informed as to what's going on.
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.
There are certain types of questions that can be simply answered on Avvo, while there are others that require considerably more analysis. You owe it to yourself to contact a lawyer. Try the lawyers used by your prospective employer first. If you are not satisfied with those answers, you can always contact an immigration lawyer, whether myself or one of my colleagues. If you appreciate the time spent preparing this answer, kindly consider marking it BEST ANSWER or HELPFUL. Also, please be sure to read my disclaimer below. Good luck to you.
Dean P. Murray
The Murray Law Firm
560 Sylvan Avenue
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Mr. Murray's response is NOT legal advice and does NOT create an attorney-client relationship. You should NOT rely on this response. Mr. Murray's response was generated without conducting a full inquiry as would occur during a face to face attorney-client consultation. It is likely that the response above may be made less accurate, or become entirely inaccurate, as you, i.e. the questioner, disclose additional facts that should only be discussed during a private consultation with an attorney. I strongly recommend that you consult an attorney who is licensed to practice law in your state (or, in the case of immigration law, and attorney in ANY state), whereupon all relevant facts will be discussed. All responses posted by Mr. Murray on Avvo.com are intended as general information for the education of the public, and not for any specific individual.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.
If the I-140 based on the EB-2 was approved, you will be able to capture the priority date for the EB-3. If you go back to an EB-2, the same will apply.
I would consult with a business immigration attorney to review your matter. This would be my best advise in your case.