Cell growth is a complex process in which cells synthesize cellular components while they increase in size. It is generally assumed that the rate of biosynthesis must somehow be coordinated with the rate of growth in order to maintain intracellular concentrations. However, little is known about potential feedback mechanisms that could achieve proteome homeostasis or the consequences when this homeostasis is perturbed. Here, we identify conditions in which fission yeast cells are prevented from volume expansion but nevertheless continue to synthesize biomass, leading to general accumulation of proteins and increased cytoplasmic density. Upon removal of these perturbations, this biomass accumulation drove cells to undergo a multi-generational period of "supergrowth" wherein rapid volume growth outpaced biosynthesis, returning proteome concentrations back to normal within hours. These findings demonstrate a mechanism for global proteome homeostasis based on modulation of volume growth and dilution.