First, "more than one" and "many" are acceptable meanings for "multiple."
1 : consisting of, including, or involving more than one: multiple births, multiple choices
2 : MANY, MANIFOLD multiple achievements: He suffered multiple injuries in the accident.
We could stop there, but we can do better. "Multiple," many authorities and kibitzers contend, is best used to describe separation, repetition, or division from a whole. Most of Merriam-Webster's definition carry this idea of repetition. Michael Kandel of the MLA agrees`:
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.
A deft writer can express herself vividly by precisely using "multiple" when it's called for. It's correct to use "multiple" to mean "more than one," but I think it's less than industrious.
In my experience, in the past twenty years writers have come to use "multiple" as a fancier, more authoritative way to say "many." Kandel suggests that this usage fits squarely into Bryan Garner's definition of jargon: use the longer word when the shorter one will do.
In a stale thread in English Forward, more than a few (and here I might well say "multiple," though "many" or "a lot" is fine) commenters vent on the bloated use of "multiple." One mirrors the prescriptive, grumpy old man in me, at least on this topic:
I am getting increasingly irritated by the indiscriminate use of the word "multiple" when a few, many or several will do: multiple gun shots; multiple perpetrators; multiple bruises, etc. It has taken over in the media because it sounds more important.
(I'm not sure, but English Forward appears to be British.)
The spokesperson said that the pursuit lasted for more than two hours and resulted in multiple near collisions involving other drivers, pedestrians and the NYPD. —Victoria Murphy, Town & Country, 18 May 2023
Read many. The idea here is that the pursuit caused numerous accidents, not repeated or similar.
Poets should aim for each reader to have multiple ways to navigate a poem. —Elizabeth Myong, Dallas News, 18 May 2023
Ok with multiple. One people engendering different interpretations.
McKean said the food truck drew patrons from multiple bars in the area despite El Chila's best efforts to clear the parking lot. —The Indianapolis Star, 17 May 2023
Clearly many. It might be good food after a night of drinking, but the only point is that there are a lot of drunks, not that they are varied or distinct.