No. Describe the additional employment and have the necessary process assessed before starting. Existing permission should not be treated as unrestricted professional work authorization.
Keep the second proposal visible
Identify whether the first role continues and how the actual duties differ. A limited schedule or similar title does not eliminate the need to assess the new arrangement.
TN eligibility requires Canadian or Mexican citizenship, prearranged professional-level business activity for a U.S. or foreign employer, and the listed profession’s particular education, licence, or experience rule; Canadian permanent residence is not citizenship. Provide the leave letter, the original support letter describing the professional duties, and the admission or approval records, so the advice rests on documents rather than descriptions. The principal’s own eligibility rests on citizenship of Canada or Mexico, a position matching a listed professional occupation in the USMCA appendix and that profession’s credential, with the work done for a US employer rather than a business the applicant controls. Canadian or Mexican citizenship, temporary entry and permitted prearranged professional work remain necessary; neither a customer’s urgency nor technical equipment replaces those conditions.