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In this study, we inquired the cross-diffusion effects on the magnetohydrodynamic Williamson fluid flow across a variable thickness stretching sheet by viewing velocity slip. With the aid of Runge-Kutta based shooting process, we resolved the transformed differential equations numerically. The effects of different dimensionless parameters on three usual profiles (velocity, temperature, concentration) along with skin friction coefficient, heat transfer rate and mass transfer rate are examined with the support of plots and tables. Dual solutions are exhibited for two cases i.e., Newtonian fluid and non-Newtonian fluid. Results reveal that the Soret and Dufour numbers have drift to control the thermal and concentration boundary layers. We also found a good agreement of the present results by comparing with the published results.