Single-cell screens enable high-throughput functional assessment of enhancers in their endogenous genomic context. However, the design of current studies limits their application to identifying the primary gene targets of enhancers. Here, we improve the experimental and computational parameters of single-cell enhancer screens to identify the secondary gene targets of enhancers. Our analysis of >500 putative enhancers in K562 cells reveals an interwoven enhancer-driven gene regulatory network. We find that enhancers from distinct genomic loci converge to modulate the expression of common sub-modules, including the α- and β-globin loci, by directly regulating transcription factors. Our analysis suggests that several genetic variants associated with myeloid blood cell traits alter the activity of a distal enhancer of MYB (∼140 kb away), with downstream consequences on hemoglobin genes expression and cell state. These data have implications for the understanding of enhancer-associated traits and emphasize the flexibility of controlling transcriptional systems by modifying enhancer activity. Display omitted •Improving single-cell screens to identify the secondary gene targets of enhancers•Applying single-cell screens to measure the activities of >500 enhancers•Enhancers across the genome converge to regulate the expression of common modules•Linking genetic variants at enhancers to trait-associated secondary gene targets Xie et al. apply improved strategies for single-cell screens to identify an enhancer-driven transcriptional regulatory network in K562 cells. They demonstrate that the same group of genes can be indirectly regulated by enhancers from distinct genomic loci. These data have implications for the understanding of enhancer-associated traits.