Reactors or crystallizers synthesizing valuable particles can be formally described by combining the laws of continuum transport theory with a population balance equation governing evolution of the "dispersed" (suspended) particle population. Early examples necessarily focused on highly idealized device configurations and populations described locally using only one particle state variable, i.e., "size" (length or volume). However, in almost every application of current/future importance, a multivariate description is required, for which the existing literature offers little guidance. We describe here our recent research on an instructive bivariate prototype of physical interest (coagulating, sintering nanoparticles of prescribed composition, etc.) that will, hopefully, motivate a broader attack on important multivariate population balance problems, including those describing continuous molecular mixtures. We illustrate the use of both physically based bivariate "mixed" moment and Monte Carlo simulation methods amenable to future generalization. Multivariate extensions, improved and fully coupled rate laws, and consideration of interacting (coexisting) populations will be required to deal with future sol reaction engineering problems using similar strategies/techniques.