Locally verifiable aggregate signatures (LVAS) enable efficient verification of aggregate signatures. When aggregate signatures reduce the space for storing signatures from linear in N to a fixed constant, local verifiability provides efficient verification. However, its main drawback is that it can only aggregate signatures on messages associated with a single signer. In this work, we extend LVAS to multi-signer settings, allowing the aggregate signature to verify that all the n users signed their respective n messages. More importantly, the verifier can determine whether a specific message is part of the set without access to the entire message list. The multi-signer locally verifiable aggregate signatures provide more flexibility in collaborative aggregate signatures among multiple users. Furthermore, we construct a multi-signer locally verifiable aggregate signature scheme from leveled multilinear maps that achieves full security based on the \((\ell ,k)\) -MDHI assumption in the random oracle model.