Yes you can do that, your work authorization is not employer specific.
Due to the nature of this forum, Attorney Maria J. Marty does not have all the information required to provide legal advice. Accordingly, her responses on Avvo are intended as general and not legal advice.
Yes, you can do all of that with the employment authorization card which your lawyer mist have filed for and obtained on your behalf. That work permit enables you to work anywhere and for whomever.
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.