The Kampmann–Wagner numerical (KWN) model, which has been widely adopted as a precipitation modeling framework accounting for concurrent nucleation, growth and coarsening kinetics, was extended to predict the as-cast grain size of inoculated multicomponent aluminum alloys. In the model, the heterogeneous nucleation of grains on inoculant particles was modeled based on the free growth criterion, while the influence of the solute on the nucleation behavior, in terms of the solute suppressed nucleation (SSN) effect, was rigorously defined and integrated. In order to fully address the solidification behavior of multicomponent alloys, a coupling of the KWN model to CALPHAD was carried out. These extensions allow the treatment of two different nucleation-ceasing mechanisms induced by grain growth: recalescence stifling and solute segregation stifling. Given melt composition, inoculation and heat extraction rate, the model is able to predict maximum nucleation undercooling, cooling curve and the final as-cast grain size of multicomponent alloys without invoking the binary equivalence assumption used in the existing models. The proposed model was tested with a variety of binary and multicomponent aluminum alloys, and the predictions were compared with the experimental measurement results and previous grain size prediction models. The simulation results show that the SSN effect has a negligible influence on the nucleation behavior and the final grain size during isothermal melt solidification, but a strong influence on the ceasing of grain nucleation during directional solidification. Reasonable agreement was obtained between the model prediction and measurement results on a direct chill casting experiment of an AA5182 alloy. Our work proves that the application of the precipitation modeling framework for the solidification problem is successful.