Interactions among drugs play a critical role in the killing efficacy of multi-drug treatments. Recent advances in theory and experiment for three-drug interactions enable the search for emergent interactions-ones not predictable from pairwise interactions. Previous work has shown it is easier to detect synergies and antagonisms among pairwise interactions when a rescaling method is applied to the interaction metric. However, no study has carefully examined whether new types of normalization might be needed for emergence. Here, we propose several rescaling methods for enhancing the classification of the higher order drug interactions based on our conceptual framework. To choose the rescaling that best separates synergism, antagonism and additivity, we conducted bacterial growth experiments in the presence of single, pairwise and triple-drug combinations among 14 antibiotics. We found one of our rescaling methods is far better at distinguishing synergistic and antagonistic emergent interactions than any of the other methods. Using our new method, we find around 50% of emergent interactions are additive, much less than previous reports of greater than 90% additivity. We conclude that higher order emergent interactions are much more common than previously believed, and we argue these findings for drugs suggest that appropriate rescaling is crucial to infer higher order interactions.