Should the phrase be "one or more is...", or "one or more are..."?
The Oxford Living Dictionaries says the following, about the usage of or. (Similar definition was given from the NOAD I had installed on my Mac Mini, the copy that comes with the Dictionary application together the OS.)
Where a verb follows a list separated by or, the traditional rule is that the verb should be singular, as long as the things in the list are individually singular, as in a sandwich or other snack is included in the price (rather than a sandwich or other snack are included in the price). The argument is that each of the elements agrees separately with the verb. The opposite rule applies when the elements are joined by and—here the verb should be plural: a sandwich and a cup of coffee are included in the price. These traditional rules are observed in good English writing style but are often disregarded in speech.
In a sentence like one or more photos are better you use are because the noun closer to the verb is plural (more photos).
There is no general agreement on whether or not the phrase "one or more" should be taken to be singular or plural.
The Cambridge Guide to English Usage says: For most writers the choice depends on whether you’re thinking of a single case or general principle. Usage commentators in the UK and the US have been inclined to say it should be plural; and the Harper–Heritage usage panel voted heavily in its favor (78%). Yet Webster’s English Usage (1989) found ample American evidence for the singular construction, and it’s just as common as the plural in British data from the BNC. Writers using the singular take their cue from one, whereas the plural-users are responding to those [people] or the [things]. (BNC stands for British National Corpus. It is a computer database of 100 million words.)
I prefer the plural usage (one or more are), taking my cue from "one or more people" or "one or more workmen" rather than the unnatural sounding (to my ear), "one or more person" or "one or more workman."
At englishforums.com, the redoubtable paco says: [tidied, EA]
... [The] question you raised is related to the issue of subject-verb concord (or agreement). ... grammar books say the following about concord:
In English the usages addressed in the area of subject-verb concord are explicable by considering the interaction of three fundamental rules: (1) the "grammatical rule", (2) the "notional rule" and (3) the "proximity rule".
(1) The grammatical rule is simply "attach singular verbs to non-plural nouns and plural verbs to plural nouns". egs
This apple is delicious but those lemons are sour.
English is a tough language to learn.
(2) The notional rule is "use plural verbs where it is felt that the individual members implied by a collective noun are implied to be directly involved, rather than the group as a whole". (synesis) eg
The audience have got tired of his speech.
(3) The proximity rule is "choose the verbal form to agree with the form of the nearest noun in the subject noun phrase". eg
John, or his brothers, have cleared the loft.
[One] complicating factor is that these three rules often conflict with each other and the priority for making the choice in such a case can vary, depending on the speaker. [(eg should synesis, and the proximity rule, even be allowed) (Others are the subjectiveness that may inform the decision of individualness or not in choosing where to employ synesis with collective nouns, and other related singular-plural grey areas / idiosyncrasies such as with: data, confetti, police; Can you eat three Shredded Wheat? – No, two Shredded Wheat are all I can manage – The Shredded Wheat is on the table – The Corn Flakes are on the table. Again, the proximity rule needs refining for cases such as: John, or his brothers, have cleared the loft.)]
With the example "More than one of my students is / are American": I guess, if you opt for "more than one of my students are American", you are choosing the verbal form according to the proximity rule, but you would say "more than one student is American" according to the grammatical rule rather than to the notional rule, regarding more as uncount.
With one or more is / are, the first thing to consider is whether 'one or more' is a unit or analysable. It has the near-synonym 'some'; 'four or five' could be substituted reasonably by 'several'. If the substitution of 'some' for 'one or more' is taken as binding, by analogy, we require plural concord.
If, on the other hand, 'one or more' is deemed not to be a single lexeme, we have to decide which rule of concord should take precedence.
Here is a relevant quote from CS Lewis on the accepted use of the proximity principle when the (other) 'rules' would argue against such usage: "Don't take any notice of teachers and text-books in such matters. Nor of logic. It is good to say 'More than one passenger was hurt,' although more than one equals at least two and therefore logically the verb ought to be plural were not singular was!" (C.S. Lewis, letter to Joan, June 26, 1956. C. S. Lewis' Letters to Children, ed. by Lyle W. Dorsett and Marjorie Lamp Mead. Touchstone, 1995).
A snag is that we would also usually say 'More than one of the passengers was hurt.' - this follows a 'displaced proximity' rule!
Perhaps expressions such as more than one, quite a few, one or more, two or fewer ... should be treated as multi-word quantifiers with idiosyncratic concord.
This is, after all, true for single-word quantifiers:
Every man has his price. All men have their price.