How is "a great many" grammatical?Many being modified by great in this case is something I have never heard before. I would say "wrote a great number of plays" or "wrote a lot of plays", maybe even "wrote very (adverb) many plays" although this is already something that I would look to avoid but "a great many plays" sounds very strange.
a great many: with pl. v.]
an extremely large number (of persons or things)
In this example 'great' is simply making certain that the reader understands that it is more than 'many'.
From Google Dictionary
1.of an extent, amount, or intensity considerably above the normal or average. "the article was of great interest"
synonyms: considerable, substantial, significant, appreciable, special, serious