<p>This study investigates the magnetohydrodynamic flow of a dusty micropolar fluid along a deformable permeable elastic surface, accounting for the effects of wall mass flux, microrotation, and fluid-particle interactions. Through an analytical approach, the existence of unique, dual, and triple solutions for velocity, skin friction, and thermal profiles is established. The findings demonstrate that for a stretching surface, a unique solution is maintained for the suction case, whereas for a shrinking surface, dual or triple solutions emerge depending on the suction or injection parameter. Notably, a critical mass flux value is identified, below which no physical solution exists. The study further highlights that increasing the fluid-particle interaction parameter enhances velocity profiles for both stretching and shrinking cases. Moreover, strong suction leads to multiple temperature solution branches, reflecting the complex thermal behavior in micropolar dusty fluids. The influence of a magnetic field is found to enhance both velocity and temperature distributions. These findings provide critical insights for controlling particle deposition and heat transfer in advanced manufacturing processes like polymer sheet extrusion and MHD-based coating technologies. The identified multiple solutions and critical thresholds offer direct design principles for optimizing system performance and avoiding operational failure in industrial applications involving micropolar dusty fluids.</p>