Klebsiella pneumoniae causes severe lung and bloodstream infections that are difficult to treat due to multidrug resistance. We hypothesized that antimicrobial resistance can be reversed by targeting chromosomal non-essential genes that are not responsible for acquired resistance but essential for resistant bacteria under therapeutic concentrations of antimicrobials. Conditional essentiality of individual genes to antimicrobial resistance was evaluated in an epidemic multidrug-resistant clone of K. pneumoniae (ST258). We constructed a high-density transposon mutant library of >430,000 unique Tn5 insertions and measured mutant depletion upon exposure to three clinically relevant antimicrobials (colistin, imipenem or ciprofloxacin) by Transposon Directed Insertion-site Sequencing (TraDIS). Using this high-throughput approach, we defined three sets of chromosomal non-essential genes essential for growth during exposure to colistin (n = 35), imipenem (n = 1) or ciprofloxacin (n = 1) in addition to known resistance determinants, collectively termed the “secondary resistome”. As proof of principle, we demonstrated that inactivation of a non-essential gene not previously found linked to colistin resistance (dedA) restored colistin susceptibility by reducing the minimum inhibitory concentration from 8 to 0.5 μg/ml, 4-fold below the susceptibility breakpoint (S ≤ 2 μg/ml). This finding suggests that the secondary resistome is a potential target for developing antimicrobial “helper” drugs that restore the efficacy of existing antimicrobials.