The systematic functional analysis of combinatorial genetics has been limited by the throughput that can be achieved and the order of complexity that can be studied. To enable massively parallel characterization of genetic combinations in human cells, we developed a technology for rapid, scalable assembly of high-order barcoded combinatorial genetic libraries that can be quantified with high-throughput sequencing. We applied this technology, combinatorial genetics en masse (CombiGEM), to create high-coverage libraries of 1,521 two-wise and 51,770 three-wise barcoded combinations of 39 human microRNA (miRNA) precursors. We identified miRNA combinations that synergistically sensitize drug-resistant cancer cells to chemotherapy and/or inhibit cancer cell proliferation, providing insights into complex miRNA networks. More broadly, our method will enable high-throughput profiling of multifactorial genetic combinations that regulate phenotypes of relevance to biomedicine, biotechnology and basic science.