Cells with complex aneuploidies display a wide range of phenotypic abnormalities. However, the molecular basis for this has been mainly studied in trisomic (2n+1) and disomic (n+1) cells. To determine how karyotype affects proliferation in cells with complex aneuploidies, we generated 92 2n+x yeast strains in which each diploid cell has between 3 and 12 extra chromosomes. Genome-wide and, for individual protein complexes, proliferation defects are caused by the presence of protein complexes in which all subunits are balanced at the 3-copy level. Proteomics revealed that over 50% of 3-copy members of imbalanced complexes were expressed at only 2n protein levels, whereas members of complexes in which all subunits are stoichiometrically balanced at 3 copies per cell had 3n protein levels. We validated this finding using orthogonal datasets from yeast and from human cancers. Taken together, our study provides an explanation of how aneuploidy affects phenotype.