NOT A TEACHER
Hi,
I thought that you might like to know the opinion of my most admired grammarian, Dr. George Oliver Curme. Here are some ideas from his two-volume masterpiece A Grammar of the English Language (1931). He uses the names of the traditional parts of speech.
Volume I, page 175
1. He says that "more than" (as used in your kind of sentence) is an adverb. His examples: "More than one has found it" and "There is more than one reason."
2. But he feels that "more" is a plural indefinite pronoun in "There are more than one."
Volume II, page 59
3. Dr. Curme says that the adverb "more than" = "not merely."
4. He points out, however, that some grammarians consider the word "more" as a plural indefinite pronoun, so they use the plural verb: "More than one have found it so" instead of "More than one has found it so."
a. He reminds us that "Of course, the plural is used when the words are separated" as in "More have found it so than just he."
P.S. I hope that you continue to post questions in the diagramming sub-forum. When I first become a member some years back, there used to be a few members who regularly posted Reed-Kellogg diagrams. It was such fun! (I am too computer illiterate to do so.)