An extended version of the mass transfer model by Reuvers et al. for a four-component system is evaluated, which is shown to be generally valid for short times. The thermodynamics under these circumstances are evaluated, together with the kinetics. Initial composition paths (concentration profiles) are calculated. It appears that delay of demixing is not possible when a polymeric additive is used, which is soluble in the nonsolvent, while the velocity of demixing decreases. The calculations are evaluated for the system poly(ether sulfone)-poly(vinylpyrrolidone)-N-methylpyrrolidone-water by means of light transmission measurements during immersion precipitation, for a wide range of compositions of the polymer solution and coagulation bath.