Cells that contain an abnormal number of chromosomes are called aneuploid. High rates of aneuploidy in cancer are correlated with an increased frequency of chromosome missegregation, termed chromosomal instability (CIN). Both high levels of aneuploidy and CIN are associated with cancers that are resistant to treatment. Although aneuploidy and CIN are typically detrimental to cell growth, they can aid in adaptation to selective pressures. Here, we induced extremely high rates of chromosome missegregation in yeast to determine how cells adapt to CIN over time. We found that adaptation to CIN occurs initially through many different individual chromosomal aneuploidies. Interestingly, the adapted yeast strains acquire complex karyotypes with specific subsets of the beneficial aneuploid chromosomes. These complex aneuploidy patterns are governed by synthetic genetic interactions between individual chromosomal abnormalities, which we refer to as chromosome copy number interactions (CCNIs). Given enough time, distinct karyotypic patterns in separate yeast populations converge on a refined complex aneuploid state. Surprisingly, some chromosomal aneuploidies that provided an advantage early on in adaptation are eventually lost due to negative CCNIs with even more beneficial aneuploid chromosome combinations. Together, our results show how cells adapt by obtaining specific complex aneuploid karyotypes in the presence of CIN.