Outsourcing an increasing amount of data to a third party raises a number of security and privacy challenges, namely remote data integrity verification. Indeed, proofs for data possession checking address the verification that some previously outsourced data blocks across multiple storing nodes are correctly stored and fully available. In this paper, we propose a new set homomorphic proof of data possession, referred to as SHoPS, supporting several operations like aggregation of proofs. SHoPS is a deterministic Proof of Data Possession (PDP) scheme, based on an interactive proof protocol. Our approach has several advantages. First, it enables several proofs to be aggregated and a subset of data files' proofs to be verified, while providing an attractive communication overhead. Second, it supports public verifiability where the verification process can be delegated to another entity, thus releasing the data owner from the cumbersome task of periodical verifications. Third, SHoPS is efficient and provably secure, as it is resistant to the fraudulence of the prover and the leakage of verified data. Finally, a theoretical performances' analysis shows that SHoPS performs better in terms of functionality, communication and computation overhead compared to closely related works and experimental results point out the applicability of the proposed scheme in real world scenarios