The expression of inhibitory immune checkpoint molecules, such as programmed death-ligand (PD-L)1, is frequently observed in human cancers and can lead to the suppression of T cell-mediated immune responses. Here, we apply expanded CRISPR-compatible (EC)CITE-seq, a technology that combines pooled CRISPR screens with single-cell mRNA and surface protein measurements, to explore the molecular networks that regulate PD-L1 expression. We also develop a computational framework, mixscape, that substantially improves the signal-to-noise ratio in single-cell perturbation screens by identifying and removing confounding sources of variation. Applying these tools, we identify and validate regulators of PD-L1 and leverage our multimodal data to identify both transcriptional and post-transcriptional modes of regulation. Specifically, we discover that the Kelch-like protein KEAP1 and the transcriptional activator NRF2 mediate the upregulation of PD-L1 after interferon (IFN)-γ stimulation. Our results identify a new mechanism for the regulation of immune checkpoints and present a powerful analytical framework for the analysis of multimodal single-cell perturbation screens.