Verified answer

Paulina's answer has no element of truth to it. Zero. Plus, the TN classification is not only for Canadians. Mexicans can also be TNs, but they need a visa stamped on a page of their passport. Canadians are exempt the visa requirement, but all the other rules are the same.

One of those rules says: A citizen of Canada or Mexico admitted into the United States as a TN nonimmigrant who seeks to change or add a United States employer during the period of admission must have the new employer file a Form I–129 with appropriate supporting documentation, including a letter from the new employer describing the services to be performed, the time needed to render such services, and the terms of remuneration for services. Employment with a different or with an additional employer is not authorized prior to Department approval of the request.

yes

Restrictions on Employment

Under federal regulations, individuals in TN status are permitted to work only for the employer who sponsored their status in the specific job requested at the time of entry. Holders of TN status are not permitted to be employed or receive compensation from any other source. If an individual wishes to work for an additional employer, or to change employers, he or she must return to Canada and apply for TN status for the new employer at the time of re-entry

TN and H1B on Canadian passport works like a green card. A Canadian can never be barred or stopped to enter US so green card in normally not required.