Multi-Party Private Set Intersection (MPSI) is an attractive topic in research since a practical MPSI protocol can be deployed in several real-world scenarios, including but not limited to finding the common list of customers among several companies or privacy-preserving analyses of data from different stakeholders. Several solutions have been proposed in the literature however, the existing solutions still suffer from performance related challenges such as long run-time and high bandwidth demand, particularly when the number of involved parties grows. In this paper, we propose a new approach based on threshold additively homomorphic encryption scheme, e.g., Paillier, which enables us to process the bit-set representation of sets under encryption. By doing so, it is feasible to securely compute the intersection of several data sets in an efficient manner. To prove our claims on performance, we compare the communication complexity of our approach with the existing solutions and show performance test results. We also show how the proposed protocol can be extended to securely compute other set operations on multi-party data sets.