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Many researchers have defined the <i>q</i>-analogous of differential and integral operators for analytic functions using the concept of quantum calculus in the geometric function theory. In this study, we conduct a comprehensive investigation to identify the uses of the Sălăgean <i>q</i>-differential operator for meromorphic multivalent functions. Many features of functions that belong to geometrically defined classes have been extensively studied using differential operators based on <i>q</i>-calculus operator theory. In this research, we extended the idea of the <i>q</i>-analogous of the Sălăgean differential operator for meromorphic multivalent functions using the fundamental ideas of <i>q</i>-calculus. With the help of this operator, we extend the family of Janowski functions by adding two new subclasses of meromorphic <i>q</i>-starlike and meromorphic multivalent <i>q</i>-starlike functions. We discover significant findings for these new classes, including the radius of starlikeness, partial sums, distortion theorems, and coefficient estimates.