Aneuploidy causes a proliferative disadvantage in all normal cells analyzed to date, yet this condition is associated with a disease characterized by unabated proliferative potential, cancer. The mechanisms that allow cancer cells to tolerate the adverse effects of aneuploidy are not known. To probe this question, we identified aneuploid yeast strains with improved proliferative abilities. Their molecular characterization revealed strain-specific genetic alterations as well as mutations shared between different aneuploid strains. Among the latter, a loss-of-function mutation in the gene encoding the deubiquitinating enzyme Ubp6 improves growth rates in four different aneuploid yeast strains by attenuating the changes in intracellular protein composition caused by aneuploidy. Our results demonstrate the existence of aneuploidy-tolerating mutations that improve the fitness of multiple different aneuploidies and highlight the importance of ubiquitin-proteasomal degradation in suppressing the adverse effects of aneuploidy.