The drug interaction terminology (synergy, additivity, antagonism) relates to bacterial kill. The suppression of resistance requires greater drug exposure. We examined the combination of meropenem and tobramycin for kill and resistance suppression (wild-type Pseudomonas aeruginosa PAO1 and its isogenic MexAB-overexpressed mutant). The drug interaction was additive. The introduction of MexAB overexpression significantly altered the 50% inhibitory concentration of meropenem but not that of tobramycin, resulting in the recovery of a marked increase in colony numbers from drug-containing plates. For the wild type, more tobramycin-resistant isolates than meropenem-resistant isolates were present, and the tobramycin-resistant isolates were harder to suppress. MexAB overexpression unexpectedly caused a significant increase in the number of tobramycin-resistant mutants, as indexed to the area under the curve of slices through the inverted U resistance mountain. The differences were significant, except in the absence of meropenem. We hypothesize that the pump resulted in the presence of less meropenem for organism inhibition, allowing more rounds of replication and also affecting the numbers of tobramycin-resistant mutants. When resistance suppression is explored by combination chemotherapy, it is important to examine the impacts of differing resistance mechanisms for both agents.