<p>The mediated semi-quantum key distribution (M-SQKD) protocol is an interesting class of quantum cryptographic protocols that, with the assistance of a third-party quantum server, allows two users to establish a string of secure key with fewer quantum devices. Numerous studies have shown that the protocol remains valid even if the server is an adversary. Subsequently, a multi-mediated SQKD protocol (MM-SQKD) emerged, allowing multiple servers to collaborate in generating keys. Although this model improves the noise tolerance of the M-SQKD protocol, it expends the qubit efficiency. In this paper, we propose a new MM-SQKD protocol that is four times more efficient than the original MM-SQKD protocol when two mediators are working. Furthermore, we derive a bound on the key rate of the proposed protocol and give its noise tolerance. The protocol will be aborted when two legitimate users observe that the key error exceeds the noise tolerance.</p>