Genetic engineering of immune cells has opened new avenues for improving their functionality but it remains a challenge to pinpoint which genes or combination of genes are the most beneficial to target. Here, we conduct High Multiplicity of Perturbations and Cellular Indexing of Transcriptomes and Epitopes (HMPCITE-seq) to find combinations of genes whose joint targeting improves antigen-presenting cell activity and enhances their ability to activate T cells. Specifically, we perform two genome-wide CRISPR screens in bone marrow dendritic cells and identify negative regulators of CD86, that participate in the co-stimulation programs, including Chd4, Stat5b, Egr2, Med12, and positive regulators of PD-L1, that participate in the co-inhibitory programs, including Sptlc2, Nckap1l, and Pi4kb. To identify the genetic interactions between top-ranked genes and find superior combinations to target, we perform high-order Perturb-Seq experiments and we show that targeting both Cebpb and Med12 results in a better phenotype compared to the single perturbations or other combinations of perturbations.