The Septuagint and the Vulgate remove the comma after “stairs.” By the “stairs (or scaffold) of the Levites” is to be understood as an elevated platform from which they could the better address and lead the people (compare Nehemiah 8:4).
Related Commentaries of Nehemiah 9:4
Nehemiah 9:4
4 Then stood up upon the stairs,b of the Levites, Jeshua, and Bani, Kadmiel, Shebaniah, Bunni, Sherebiah, Bani, and Chenani, and cried with a loud voice unto the LORD their God.