If you've been counted against the cap in the previous six years, you are not again subject to the cap for now. You can go cap subject to cap exempt to cap subject -- assuming of course that you qualify otherwise and the filing is properly prepared.
Attorney Khurgel is a former USCIS and State Department Embassy Officer. His comments on Avvo are general advice, and do not constitute an attorney-client relationship.
As long as you counted against the cap with the first petition, you can switch back to another cap subject petition at any time as you have already been counted in the last 6 years. Assuming time in h1b status does not pose a problem and, of course, the petition is approved.
As my colleagues have pointed out, if you've been counted against the cap in the previous six years, you will not be counted against the cap again. Your sponsor will need to file a transfer (a new H1B petition) and you will need to qualify for employment with the new employer. You can start working for the new employer once USCIS receives the I-129 transfer petition.
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