Yes you can. To be on the safe side change your status to visitor visa. File your application as soon as you can.
Elkhalil Law Firm, LLC
Disclaimer: This answer is for informational and educational use only. This answer does not create attorney-client relationship. For more details, I recommend a private consultation with an immigration lawyer.
If you have already been counted against the H-1B cap, you can port to another employer as soon as the new I-129 petition has been properly filed and received by USCIS. There is no need to leave the U.S. in order to accomplish this goal. Hire a good immigration attorney to represent you if you do not already have one!
Attorney answers to questions are for general purposes only and do not establish an attorney-client relationship. Please consult with an immigration attorney to get complete answers to your legal questions.
You can have your new employer file the I-129 immediately.
You should retain an experienced immigration lawyer, whether myself or one of my colleagues, to review all the facts, advise you, and handle the case.
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.