This would be part of an incomplete sentence, because "Many of whom" suggests that there is a sentence missing in front. In a way, the words "of whom" demands an explanation who those people are- "many" is simply a modifier as you mentioned, but the question remains "who are those people?" Without an answer, the sentence example cannot be considered complete. For example: "His work is widely praised by his contemporaries, many of whom consider him the greatest jazz musician of all time."

That is a fascinating question. I'm a native US speaker, not a teacher and not a grammarian. I agree completely with Darryl Wee and his explanation, but I'm not sure about the grammar behind it. At any rate, all of these are complete and correct sentences: "Many consider him the greatest jazz musician of all time." "Many people consider him the greatest jazz musician of all time." "Many of the most respected jazz musicians consider him to be the greatest jazz musician of all time." "Many of them consider him to be the greatest jazz musician of all time." And yet, "Many of whom consider him the greatest jazz musician of all time" is bad English and does not even make sense. Furthermore, this sentence is correct: "He is admired by critics, many of whom consider him to be the best jazz musician of all time," but if you break it into two sentences, the second sentence is still bad English: "He is admired by critics. Many of whom consider him to be the greatest jazz musician of all times." This, however, is correct: "He is admired by critics. Many of them consider him to be the best jazz musician of all time." I hope someone can give an explanation based on grammatical rules, because I can't.

It's just a clause.