Eligibility turns on Canadian or Mexican citizenship, a listed profession, the credential that profession requires, prearranged professional employment and temporary entry. The number of locations is not itself the test, but the file still has to show professional duties rather than an undefined territory.
Geography is context, not the test
A multi-site assignment fails on the same grounds any assignment fails: duties that do not match a listed profession, a credential that does not meet the listing, or an employment relationship that is unclear. Describe the work first and the map second. If the territory is the only concrete thing in the letter, the underlying professional role has not yet been documented.
Compare the citizenship condition against permanent residence, because the two are routinely confused. TN is open to citizens of Canada or Mexico; a permanent resident of Canada who holds another nationality does not qualify on that basis and would be looking at a different category entirely. Weigh the role against a business visitor's activities as well: attending meetings, negotiating or taking orders can sit within visitor status, while performing the professional work itself does not.
Hypothetical example: an engineer is asked to spend several weeks at United States maintenance facilities commissioning avionics test benches. That is professional work being performed rather than a business visit, so the route has to be settled before departure instead of at the border.