Topological constraint theory holds the key to understanding the temperature and composition dependence of the dynamics of glass-forming liquids. Unfortunately, existing analytical models currently do not apply to multicomponent industrial glasses. Moreover, models that are strictly empirical in nature fail to provide insight into the underlying physical trends and cannot extrapolate beyond the compositional ranges used for fitting of their parameters. In this paper, we present a phenomenological model offering an improved description of the composition and temperature dependence of the shear viscosity of multicomponent liquids. The model has a clear physical foundation based on the temperature dependence of the network constraints with only two empirical fitting parameters per oxide component. The model predicts the isokom temperatures of 7141 viscosity measurements for 760 different compositions with a root-mean-square error of only 6.55 K.