Both “multiples” and “multiple” are correct when you want to discuss an object in a general numerical value that’s higher than one. These can both be nouns or adjectives depending on where it is in a sentence. However, it doesn’t sound phonetically correct to use –s with “multiple” as an adjective.
It’s not a difficult thing to commit to memory. But, you do have to remember the differences between what an adjective is versus a noun.
Grammar; Meaning of “Multiple”
In general, “multiple” is a word to indicate numeric integers (a noun) or it describes more than one of something with a broad reference (an adjective).
36 is a multiple of nine. [noun]
This contains multiple data points. [adjective]
“Multiples”; “Multiple”
When making “multiple” plural by adding –s at the end of the word, it is only a noun. Consider the examples below:
Singular: There is a multiple of this document.
Plural: There are multiples of these documents.
In these two examples above, “multiple” becomes a noun that can be either singular or plural with a clear display of numeric agreement.
Correct: There are multiple pieces of paperwork.
Incorrect: There are multiples pieces of paperwork.
In the second set of examples, both sentences are technically correct in terms of grammar. But, “multiples pieces” doesn’t sound phonetically correct. “Multiples” registers as a qualitative plural noun and not an adjective, although its function should be an adjective.
Plural: In basic math, nine multiples of nine equal 81.
Singular: In basic math, a nine multiple is three.
These examples list “multiple” or “multiples” as a noun. When you use “multiples” as an adjective, it simply doesn’t make sense in an audible way; albeit correct in grammar and function.
Mnemonic Device
For the sake of simplicity and understanding, remember when you add an –s to “multiple,” you intend to use it as a noun (object, person, place, or thing). When you use the singular “multiple,” it is either a noun or an adjective. The general rule here is that adjectives cannot be plural, only nouns.
Multiples = adjective
Multiple = noun OR adjective
Conclusion
When you’re referring to something that has more the one, either “multiple” or “multiples” are correct as a noun. If you want to describe a noun by using an adjective, then the only correct form (that will also sound right) will be “multiple.”
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