Abstract <p>The dynamics of shock wave collisions in a strongly coupled dusty plasma consisting of inertial negatively charged dust grains, Maxwellian distributed electrons and ions was investigated. Employing the extended Poincaré–Lighthill–Kuo method, a couple of Burgers’ equations are derived to describe the evolution of dust acoustic shock waves in the presence of strong coupling and dissipation. The one-fold and two-fold solutions of coupled Burgers’ equations are systematically described through Hirota’s bilinear formalism, allowing for an analytical exploration of nonlinear interactions between shock structures. The study reveals that the shock wave collisions exhibit distinct features influenced by the fold structure, such as variations in amplitude, width, and waveform shape, as determined through an analysis of temporal behavior and the impact of collision frequency on the plasma system’s morphology and dynamics. Three-dimensional visualizations further illustrate the parametric dependence of shock interactions, providing deep insight into the collective behavior of nonlinear structures in strongly coupled dusty plasmas.</p>