This work considers an n-party private set intersection (nPSI) problem and presents a corresponding practical protocol that is secure in the semi-honest model. Although the nPSI problem has already some solutions, they become inefficient in the real-life applications, especially when they run over multiple dynamic datasets whose elements are frequently updated. This motivates our work to circumvent this problem and obtain a practically meaningful result. To this end, we extend Agrawal et al.'s 2-party protocol to an nPSI protocol without compromising its practical efficiency. We provide the complexity to show that our construction efficiently runs over dynamic datasets.