The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The model is based upon higher-order moment equations of kinetic theory of mixtures, which include viscous dissipation in the model. Governing equations are analyzed in a scaled form, which introduces the proper orders of magnitude of each term. In the socalled diffusive scaling, the Mach and Knudsen numbers are assumed to be of the same small order of magnitude. In the asymptotic limit when the small parameter vanishes, the model exhibits a coupling between the species' partial pressure gradients, which generalizes the classical model. Scaled equations also lead to a higher-order model of diffusion with correction terms in the small parameter. In that case, the viscous tensor is determined by genuine balance laws.