Combination therapy aims to prevent growth of organisms not resistant to all component drugs, making it an obvious strategy for countering the global rise of multi-drug resistance. However, success relies on preventing resistance from arising to all component drugs before full inhibition is reached during treatment. Here, we investigated whether bacterial populations can overcome combination therapy by evolving 'multi-resistance', i.e. independent resistance mutations to multiple drugs, during single-drug and combination antibiotic treatment. Using both experimental evolution and in silico stochastic simulations, we studied resistance evolution in a common laboratory strain of bacteria (Escherichia coli K-12 BW25113). Populations were exposed to either single-drug or combination treatments involving rifampicin and nalidixic acid, with concentrations increasing through time. For wild-type populations, multi-resistance was not detected in any of the experimental populations, and simulations predict its evolution should be rare.However, populations comprising mixtures of wild-type and 'mutator' strains were readily capable of evolving multi-resistance. Increasing the initial frequency of mutators resulted in a higher proportion of populations evolving multi-resistance. Experiments and simulations produced the same qualitative-and in many cases, quantitative-insights about the association between resistance, mutators and antibiotic treatment. In particular, both approaches demonstrated that multi-resistance can arise through sequential acquisition of independent resistance mutations, without a need to invoke multi-drug resistance mechanisms. Crucially, we found multi-resistance evolved even when not directly favoured by natural selection, i.e. under single-drug treatments. Simulations revealed this resulted from elevated mutation supply caused by genetic hitch-hiking of the mutator allele on single-drug resistant backgrounds. Our results suggest that combination therapy does not necessarily prevent sequential acquisition of multiple drug resistances via spontaneous mutation when mutators are present. Indeed both combination and single-drug treatments actively promoted multi-resistance, meaning that combination therapy will not be a panacea for the antibiotic resistance crisis. inference, stochastic simulations, individual-based model, Markov chains W , K. B., 2016 Pairwise interactions and the battle against combinatorics in multidrug therapies.