Cop9 signalosome (CSN) regulates the function of cullin-RING E3 ubiquitin ligases (CRLs) by deconjugating the ubiquitin-like protein NEDD8 from the cullin subunit. To understand the physiological impact of CSN function on the CRL network and cell proliferation, we combined quantitative mass spectrometry and genome-wide CRISPR interference (CRISPRi) and CRISPR activation (CRISPRa) screens to identify factors that modulate cell viability upon inhibition of CSN by the small molecule CSN5i-3. CRL components and regulators strongly modulated the antiproliferative effects of CSN5i-3, and in addition we found two pathways involved in genome integrity, SCFFBXO5-APC/C-GMNN and CUL4DTL-SETD8, that contribute substantially to the toxicity of CSN inhibition. Our data highlight the importance of CSN-mediated NEDD8 deconjugation and adaptive exchange of CRL substrate receptors in sustaining CRL function and suggest approaches for leveraging CSN inhibition for the treatment of cancer.