Aneuploidy produces myriad consequences in health and disease, yet models of the deleterious effects of chromosome amplification are still widely debated. To distinguish the molecular determinants of aneuploidy stress, we measured the effects of duplicating individual genes in cells with varying chromosome duplications, in wild-type cells and cells sensitized to aneuploidy by deletion of RNA-binding protein Ssd1. We identified gene duplications that are nearly neutral in wild-type euploid cells but significantly deleterious in euploids lacking SSD1 or SSD1+ aneuploid cells with different chromosome duplications. Several of the most deleterious genes are linked to translation; in contrast, duplication of other translational regulators, including eI5Fa Hyp2, benefit ssd1Δ aneuploids over controls. Using modeling of aneuploid growth defects, we propose that the deleterious effects of aneuploidy emerge from an interaction between the cumulative burden of many amplified genes on a chromosome and a subset of duplicated genes that become toxic in that context. Our results suggest that the mechanism behind their toxicity is linked to a key vulnerability in translation in aneuploid cells. These findings provide a perspective on the dual impact of individual genes and overall genomic burden, offering new avenues for understanding aneuploidy and its cellular consequences.