The MLA follows Merriam-Webster’s Collegiate Dictionary in using multiple to mean “consisting of, including, or involving more than one” or “many, manifold” (“Multiple, Adj.,” defs. 1 and 2 [Collegiate Dictionary]). But in my view multiple is often not a good synonym for many, meaning “a large number,” because multiple has traditionally had a narrower sense: that many elements or parts belong to or are involved in one thing or one event. The definitions of multiple in Merriam-Webster Unabridged (“Multiple, Adj.,” def. 1), The American Heritage Dictionary (“Multiple”), and the Oxford English Dictionary (“Multiple, N. and Adj.,” def. B1a) all convey the idea of connectedness.
A few examples:
A woman who gave birth to five daughters over eight years has many children.
A woman who delivered five daughters in four minutes by caesarean section had a multiple birth.
A man who broke a leg, wrist, and finger in three separate accidents suffered many broken bones.
A man who broke a leg in three places in a single accident suffered a multiple fracture.
A car that was bought and sold six times has had many owners.
When six people together own one car, their ownership is multiple.
If you are writing multiple only because many seems unsophisticated, consider Bryan Garner’s second essential rule of officialese: “[I]f a longer word (e.g., utilize) and a shorter word (e.g., use) are both available, choose the longer”—lest that admonishing finger point to you.
Garner, Bryan A. “Officialese.” Garner’s Modern American Usage, 3rd ed., Oxford UP, 2009, p. 587.
“Multiple.” The American Heritage Dictionary of the English Language, Houghton Mifflin Harcourt, 2020, ahdictionary.com/word/search.html?q=multiple.
“Multiple, Adj.” Merriam-Webster Unabridged, 2020, unabridged.merriam-Webster.com/collegiate/multiple. Collegiate Dictionary.
“Multiple, Adj.” Merriam-Webster Unabridged, 2020, unabridged.merriam-Webster.com/unabridged/multiple.
“Multiple, N. and Adj.” Oxford English Dictionary, Oxford UP, 2020, www.oed.com/view/Entry/123584.