Proteasome inhibitor (PI) resistance remains a central challenge in multiple myeloma. To identify pathways mediating resistance, we first mapped proteasome-associated genetic co-dependencies. We identified cytosolic heat shock protein 70 (HSP70) chaperones as potential targets, consistent with proposed mechanisms of myeloma tumor cells overcoming PI-induced stress. These results led us to explore allosteric HSP70 inhibitors (JG compounds) as myeloma therapeutics. We showed these compounds exhibit increased efficacy against acquired and intrinsic PI-resistant myeloma models, unlike HSP90 inhibition. Surprisingly, shotgun and pulsed-SILAC mass spectrometry found that JGs have the most pronounced effect on the proteome not through inhibiting cytosolic HSP70s but instead through mitochondrial-localized HSP70, HSPA9/mortalin, destabilizing the 55S mitoribosome. Analysis of myeloma patient data further supports strong effects of global proteostasis capacity, and particularly HSPA9 expression, on PI response. Our results characterize myeloma proteostasis networks under therapeutic pressure while motivating further investigation of HSPA9 as a specific vulnerability in PI-resistant disease.