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Cells sense a wide variety of signals and respond by adopting complex transcriptional states. Most single-cell profiling is carried out today at cellular baseline, blind to cells' potential spectrum of functional responses. Exploring the space of cellular responses experimentally requires access to a large combinatorial perturbation space. Single-cell genomics coupled with multiplexing techniques provide a useful tool for characterizing cell states across several experimental conditions. However, current multiplexing strategies require programmatic handling of many samples in macroscale arrayed formats, precluding their application in large-scale combinatorial analysis. Here, we introduce StimDrop, a method that combines antibody-based cell barcoding with parallel droplet processing to automatically formulate cell population × stimulus combinations in a microfluidic device. We applied StimDrop to profile the effects of 512 sequential stimulation conditions on human dendritic cells. Our results demonstrate that priming with viral ligands potentiates hyperinflammatory responses to a second stimulus, and show transcriptional signatures consistent with this phenomenon in myeloid cells of patients with severe COVID-19.