Combinations of three or more drugs are routinely used in various medical fields such as clinical oncology and infectious diseases to prevent resistance or to achieve synergistic therapeutic benefits. The very large number of possible high-order drug combinations presents a formidable challenge for discovering synergistic drug combinations. Here, we establish a guided screen to discover synergistic three-drug combinations. Using traditional checkerboard and recently developed diagonal methods, we experimentally measured all pairwise interactions among eight compounds in Erwinia amylovora, the causative agent of fire blight. Showing that synergy measurements of these two methods agree, we predicted synergy/antagonism scores for all possible three-drug combinations by averaging the synergy scores of pairwise interactions. We validated these predictions by experimentally measuring 35 three-drug interactions. Therefore, our guided screen for discovering three-drug synergies is (i) experimental screen of all pairwise interactions using diagonal method, (ii) averaging pairwise scores among components to predict three-drug interaction scores, (iii) experimental testing of top predictions. In our study, this strategy resulted in a five-fold reduction in screen size to find the most synergistic three-drug combinations.