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The collision of dressed dust acoustic solitons (DDASs) and the analytical higher-order phase shift are studied in a dusty plasma system that contains cold negative and positive dusty fluids and Maxwellian distributed for ions as well as electrons. The extended Poincaré–Lighthill–Kuo method is applied in order to obtain the nonlinear Korteweg–de Vries and phase shift equations, which admit the variation in soliton profiles and trajectories, respectively. Influences of the higher-order correction and the plasma fluid parameters such as charged dust grains concentration, negative-to-positive dust grain mass ratio, ion-to-negative dust grain number density ratio, and ion-to-electron temperature ratio on the characteristics of DDASs and their phase shifts are discussed. The comparisons between first- and higher-order contributions in rarefactive and compressive profiles are also taken into account. Furthermore, the present consideration may be utilised to mesosphere and magnetosphere. [ABSTRACT FROM AUTHOR]