This work focuses on sequential locally recoverable codes (SLRCs), a special family of locally repairable codes, capable of correcting multiple code symbol erasures, which are commonly used for distributed storage systems. First, we construct an extended $q$-ary family of non-binary SLRCs using code products with a novel maximum number of recoverable erasures $t$ and a minimal repair alternativity $A$. Second, we study how MDS and BCH codes can be used to construct $q$-ary SLRCs. Finally, we compare our codes to other LRCs.