Thomas R. answered 08/21/19
Over 25 years of experience and a sense of humor about math
The easiest way to research this is to visit the Internet Movie Database, then search "multiple narrators" with "keywords" selected. You will get a laundry list of films, many of which are foreign films I have not seen. Remember: you might have to consider whether you will only accept vocal narrators or also allow written narrators I remember one especially clumsy, low-budget movie that began with onscreen AND vocal narrators with totally different texts! Talk about cognitive dissonance!
One movie that famously had multiple narrators, each sharing different perspectives on the same event, was the Japanese classic "Rashomon". I don't know if it holds a record, though. Many movies with multiple narratives have had one or even no narrators (such as "Cookie's Fortune" or the classic "The Best Years of Our Lives"). I consider narration a sign of lazy writing in most movies, though the rare exceptions -- such as "The Shawshank Redemption" or "Goodfellas" -- include the narrator as a character and have the narration not only guide us through the story, but also through the narrator's evolution.
If you had included television, I would have said I was confident that the record-holder must be "The West Wing", whose episode "The Stackhouse Filibuster" had nearly the entire cast switch back-and-forth as narrators.