In distributed storage systems, locally repairable codes (LRCs) are introduced to realize low disk I/O and repair cost. In order to tolerate multiple node failures, the LRCs with \emph{$(r, δ)$-locality} are further proposed. Since hot data is not uncommon in a distributed storage system, both Zeh \emph{et al.} and Kadhe \emph{et al.} focus on the LRCs with \emph{multiple localities or unequal localities} (ML-LRCs) recently, which said that the localities among the code symbols can be different. ML-LRCs are attractive and useful in reducing repair cost for hot data. In this paper, we generalize the ML-LRCs to the $(r,δ)$-locality case of multiple node failures, and define an LRC with multiple $(r_{i}, δ_{i})_{i\in [s]}$ localities ($s\ge 2$), where $r_{1}\leq r_{2}\leq\dots\leq r_{s}$ and $δ_{1}\geqδ_{2}\geq\dots\geqδ_{s}\geq2$. Such codes ensure that some hot data could be repaired more quickly and have better failure-tolerance in certain cases because of relatively smaller $r_{i}$ and larger $δ_{i}$. Then, we derive a Singleton-like upper bound on the minimum distance for the proposed LRCs by employing the regenerating-set technique. Finally, we obtain a class of explicit and structured constructions of optimal ML-LRCs, and further extend them to the cases of multiple $(r_{i}, δ)_{i\in [s]}$ localities.