Proteasome inhibitor (PI) resistance remains a central challenge in multiple myeloma. To identify pathways mediating this resistance, we mapped genetic co-dependencies associated with the proteasome. These studies identified cytosolic heat shock protein 70 (HSP70) chaperones as a potential target, mirroring recent studies that have shown mechanism of overcoming PI-induced stress. Here, we first underscore this relationship by mapping genetic co-dependencies in cancer proteostasis. These results lead us to explore HSP70 inhibitors as potential therapeutics. We show these compounds exhibit increased efficacy against both acquired and intrinsic PI-resistant myeloma models, unlike HSP90 inhibition. Surprisingly, shotgun and pulsed-SILAC proteomics reveal that JG’s overcome PI resistance not via the expected mechanism of inhibiting cytosolic HSP70s, but instead through mitochondrial-localized HSP70, HSPA9, destabilizing the 55S mitoribosome. Analysis of myeloma patient data further supports strong effects of global proteostasis capacity, and particularly HSPA9 expression, on response to PI. Our results characterize dynamics of myeloma proteostasis networks under therapeutic pressure while further motivating investigation of HSPA9 as a specific target in PI-resistant disease. This dataset corresponds to figure 5, experiment outlined in figure 5a.