This next part of the film is exciting.
Part can be an ordinary noun with a determiner.
(A) part of the film was shot in Iceland.
(A) part of our ceiling fell down.
But we can also use part of as a quantifier without an article.
Some of the students
We normally use part of only before a singular noun.
NOT part of the students
I was out most of the day.
For a majority we use most.
NOT the most part of the day.