To survey trigenic interactions, we designed query strains that sampled key features of the global digenic interaction network: (i) digenic interaction strength, (ii) average number of digenic interactions, and (iii) digenic interaction profile similarity. In total, we tested 400,000 double and 200,000 triple mutants for fitness defects and identified 9500 digenic and 3200 trigenic negative interactions. Although trigenic interactions tend to be weaker than digenic interactions, they were both enriched for functional relationships. About one-third of trigenic interactions identified "novel" connections that were not observed in our digenic control network, whereas the remaining approximately two-thirds of trigenic interactions "modified" a digenic interaction, suggesting that the global digenic interaction network is important for understanding the trigenic interaction network. 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.