We present a theoretical formalism, which, for the first time, accounts for nucleation and growth of mineral particles of variable composition involving two independent substitutions, in aqueous solutions. It is based on the classical nucleation theory, on a size-dependent algebraic growth law allowing growth, resorption, and ripening of particles simultaneously, and on conservation laws akin to a thermodynamically closed system. Truly kinetic conditions are provided to determine the composition of the new nuclei which form and the composition of the deposited layers on the particles which were previously formed. Devised for describing the precipitation of a large range of solid solutions with double substitution, it yields the time evolution of all ion activities in the aqueous solution, together with the particle population characteristics: number, size, and composition profile of particles as a function of time and of their time of nucleation. We show that four different scenarios may take place, depending on the number of end-members involved in the chemical mixing (three or four) and depending on the particle aspect ratio, which may imply quasi two-dimensional growth, like in clay minerals, or three-dimensional growth for more compact solids like salts. This theoretical approach, in the line of our previous works made to treat precipitation of minerals of fixed composition or binary solid solutions, provides a major advance with respect to presently available solid solution precipitation models.