A joint appointment may involve qualifying prearranged professional work, but its label does not settle eligibility. Identify every actual employment relationship, the activities each covers and the relevant profession and credentials. If two employers are involved, have counsel assess the authorization needed for each before work begins. Two parties answer for different halves of that question. The entity answers for the offer and the duties; you answer for citizenship and for meeting the qualification listed against that profession. A joint arrangement does not merge those obligations, and it cannot create an authorization neither party actually holds.
Name the employer or employers precisely
Start with the contracts and proposed duties, then compare each part with the TN requirements: Canadian or Mexican citizenship, a listed profession, its credentials and temporary entry for prearranged professional work. Explain funding, supervision and payment arrangements without assuming a shared project means a single employer. A letter should not silently omit work performed for another organisation.
Hypothetical example: an engineer accepts a split arrangement in which a design firm doing waterfront facility engineering directs part of the work while a second company pays for the rest. The design firm's officer confirms the duties in writing; the engineer's own file has to establish the degree or licence the listed profession requires. When the second company declines to describe its portion, counsel advises seeking a separate authorization rather than presenting one letter as covering both.