Hallmarks of cancer, including rapid growth and aneuploidy, can result in non-oncogene addiction to the proteostasis network that can be exploited clinically. The defining example is the exquisite sensitivity of multiple myeloma (MM) to 20S proteasome inhibitors, such as carfilzomib. However, MM patients invariably acquire resistance to these drugs. Using a next-generation shRNA platform, we found that proteostasis factors, including chaperones and stress-response regulators, controlled the response to carfilzomib. Paradoxically, 19S proteasome regulator knockdown induced resistance to carfilzomib in MM and non-MM cells. 19S subunit knockdown did not affect the activity of the 20S subunits targeted by carfilzomib nor their inhibition by the drug, suggesting an alternative mechanism, such as the selective accumulation of protective factors. In MM patients, lower 19S levels predicted a diminished response to carfilzomib-based therapies. Together, our findings suggest that an understanding of network rewiring can inform development of new combination therapies to overcome drug resistance.