A new analysis of evolution of an ensemble of supercritical (in size) droplets in the atmosphere of several condensing vapors has been presented. The analysis has been performed for the nucleation stage of formation and growth of the supercritical droplets in a closed system with a fixed amount of condensing species. The nucleation stage starts with appearance of supercritical droplets and finishes when nucleation rate of new critical droplets in the closed system ceases due to vapor depletion by the growing supercritical droplets. Here, we extend the mean-field theory for the nucleation stage of gas bubbles formation at degassing of a solution of several dissolved gases, which was published recently [A. E. Kuchma et al., J. Chem. Phys. 148, 234103 (2018)], to the nucleation stage of multicomponent nucleation and growth of supercritical droplets at isothermal conditions. An approach, which allows one to find all vapor supersaturations and the distribution of supercritical droplets in sizes as functions of time on the nucleation stage, has been proposed here for a real multicomponent solution and illustrated in the case of ideal multicomponent solution in supercritical droplets.