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When more than one stands alone, it usually takes a singular verb, but it may take a plural verb if the notion of multiplicity predominates:

The operating rooms are all in good order. More than one is (or are) equipped with the latest imaging technology.

When more than one is followed by of and a plural noun, the verb is plural: More than one of the paintings were stolen.

What does multiplicity exactly mean here?

Secondly, I cannot check on Ngrams, but feel the singular is right in the second example

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Seems like you are using the American Heritage dictionary, if you then follow on to the "one" section there is a much larger discussion of the issue. There seems to be no clear answer for all cases, and there seems to be disagreement in many cases.

If the thing we are talking about is clearly singular then we can easily use the singular, and viceversa. That's what multiplicity means, if you have several, then use the plural.

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