To systematically explore complex genetic interactions, we constructed ~200,000 yeast triple mutants and scored negative trigenic interactions. We selected double-mutant query genes across a broad spectrum of biological processes, spanning a range of quantitative features of the global digenic interaction network and tested for a genetic interaction with a third mutation. Trigenic interactions often occurred among functionally related genes, and essential genes were hubs on the trigenic network. Despite their functional enrichment, trigenic interactions tended to link genes in distant bioprocesses and displayed a weaker magnitude than digenic interactions. We estimate that the global trigenic interaction network is ~100 times as large as the global digenic network, highlighting the potential for complex genetic interactions to affect the biology of inheritance, including the genotype-to-phenotype relationship.