The over-threshold multi-party private set intersection (OT-MP-PSI) protocol is a variant of the conventional PSI protocol. This protocol allows m participants to jointly compute the OT intersection for which at least t (t≤m) participants have the common element and ensures that only the participant with the OT element knows whether the element belongs to the OT intersection and nothing else. The OT-MP-PSI protocol extends the practical application scenarios of the PSI protocol. As the existing schemes are all constructed on the basis of expensive public key-based cryptography, their heavy computational burden results in long runtime. This study designs a novel cryptographic component, the oblivious programmable pseudo-random secret-sharing (OPPR-SS) component based on symmetric cryptography. Furthermore, a two cloud-assisted OT-MP-PSI protocol is designed on the basis of the OPPR-SS component, and it assigns the tasks of secret sharing and reconstructing to untrusted cloud servers, respectively, so that they can assist in the completion of those tasks. As a result, participants with weak computation capability can complete the OT-MP-PSI protocol as well. Furthermore, the study proves that the proposed protocol is secure in the semi-honest model. Compared with the existing OT-MP-PSI protocols, the proposed protocol achieves the optimal runtime and communication overhead at both the secret sharing stage and the secret reconstructing stage. The communication complexities of the participants, the secret sharing cloud, and reconstructing cloud are no longer related to the threshold t. The number of communication rounds for the participants is constant, and the communication complexity is merely O(n). The computational complexities of the secret sharing cloud and the secret reconstructing cloud are only related to the number of symmetric cryptographic operations.