The 26S proteasome conducts the majority of regulated protein catabolism in eukaryotes. At the heart of the proteasome is the barrel-shaped 20S core particle (CP), which contains two β-rings sandwiched between two α-rings. Whereas canonical CPs contain α-rings with seven subunits arranged α1-α7, a non-canonical CP in which a second copy of the α4 subunit replaces the α3 subunit occurs in both yeast and humans. The mechanisms that control canonical versus non-canonical CP biogenesis remain poorly understood. Here, we have repurposed a split-protein reporter to identify genes that can enhance canonical proteasome assembly in mutant yeast producing non-canonical α4-α4 CPs. We identified the proteasome subunit α1 as an enhancer of α3 incorporation, and find that elevating α1 protein levels preferentially drives canonical CP assembly under conditions that normally favor α4-α4 CP formation. Further, we demonstrate that α1 is stoichiometrically limiting for α-ring assembly, and that enhancing α1 levels is sufficient to increase proteasome abundance and enhance stress tolerance in yeast. Together, our data indicate that the abundance of α1 exerts multiple impacts on proteasome assembly and composition, and we propose that the limited α1 levels observed in yeast may prime cells for alternative proteasome assembly following environmental stimuli.