Alteration of normal ploidy (aneuploidy) can have a number of opposing effects, such as unbalancing protein abundances and inhibiting cell growth but also accelerating genetic diversification and rapid adaptation. The interplay of these detrimental and beneficial effects remains puzzling. Here, to understand how cells develop tolerance to aneuploidy, we subject disomic (i.e. with an extra chromosome copy) strains of yeast to long-term experimental evolution under strong selection, by forcing disomy maintenance and daily population dilution. We characterize mutations, karyotype alterations and gene expression changes, and dissect the associated molecular strategies. Cells with different extra chromosomes accumulated mutations at distinct rates and displayed diverse adaptive events. They tended to evolve towards normal ploidy through chromosomal DNA loss and gene expression changes. We identify genes with recurrent mutations and altered expression in multiple lines, revealing a variant that improves growth under genotoxic stresses. These findings support rapid evolvability of disomic strains that can be used to characterize fitness effects of mutations under different stress conditions.