Mislocalization of the centromeric histone H3 variant (Cse4 in budding yeast, CID in flies, CENP-A in humans) to noncentromeric regions contributes to chromosomal instability (CIN) in yeast, fly, and human cells. Overexpression and mislocalization of CENP-A have been observed in cancers, however, the mechanisms that facilitate the mislocalization of overexpressed CENP-A have not been fully explored. Defects in proteolysis of overexpressed Cse4 (GALCSE4) lead to its mislocalization and synthetic dosage lethality (SDL) in mutants for E3 ubiquitin ligases (Psh1, Slx5, SCFMet30, and SCFCdc4), Doa1, Hir2, and Cdc7. In contrast, defects in sumoylation of overexpressed cse4K215/216/A/R prevent its mislocalization and do not cause SDL in a psh1Δ strain. Here, we used a genome-wide screen to identify factors that facilitate the mislocalization of overexpressed Cse4 by characterizing suppressors of the psh1Δ GALCSE4 SDL. Deletions of histone H4 alleles (HHF1 or HHF2), which were among the most prominent suppressors, also suppress slx5Δ, cdc4-1, doa1Δ, hir2Δ, and cdc7-4 GALCSE4 SDL. Reduced dosage of H4 leads to defects in sumoylation and reduced mislocalization of overexpressed Cse4, which contributes to suppression of CIN when Cse4 is overexpressed. We determined that the hhf1-20, cse4-102, and cse4-111 mutants, which are defective in the Cse4-H4 interaction, also exhibit reduced sumoylation of Cse4 and do not display psh1Δ GALCSE4 SDL. In summary, we have identified genes that contribute to the mislocalization of overexpressed Cse4 and defined a role for the gene dosage of H4 in facilitating Cse4 sumoylation and mislocalization to noncentromeric regions, leading to CIN when Cse4 is overexpressed.