No. TN authorization is generally tied to a specific employer and role, so a second employer typically needs its own supporting authorization. Working for a second employer without that authorization can put both the new arrangement and the existing status at risk, so confirm the requirement before starting any second role.
Review each employer relationship separately
Even where the profession is the same for both employers, each relationship is assessed on its own facts: duties, supervision, schedule, and worksite. Confirm whether the applicant's citizenship and location call for a new border presentation or another filing for the second employer specifically. Keep the first employer's terms unchanged while pursuing the second authorization, so there is no ambiguity about what each employer relationship actually involves.
Each profession in Appendix 2 carries its own line, and those lines were written separately: a few name a state or provincial licence, most name a degree, and a small number allow years of experience with a post-secondary certificate. A second, independent finding asks whether the American position consists of professional surveying, and a role built around crew supervision and subcontractor coordination will not satisfy it however impeccable the credential is. What matters is whether the arrangement still shows a qualifying listed profession, an accepted credential, and prearranged professional employment for temporary entry, and whether any ownership interest raises the self-employment bar.