Abstract The emergence of resistance to targeted therapies restrains their efficacy. The development of rationally guided drug combinations could overcome this currently insurmountable clinical challenge. However, our limited understanding of the trajectories that drive the outgrowth of resistant clones in cancer cell populations precludes design of drug combinations to forestall resistance. Here, we propose an iterative treatment strategy coupled with genomic profiling and genome-wide CRISPR activation screening to systematically extract and define preexisting resistant subpopulations in an EGFR-driven lung cancer cell line. Integrating these modalities identifies several resistance mechanisms, including activation of YAP/TAZ signaling by WWTR1 amplification, and estimates the associated cellular fitness for mathematical population modeling. These observations led to the development of a combination therapy that eradicated resistant clones in large cancer cell line populations by exhausting the spectrum of genomic resistance mechanisms. However, a small fraction of cancer cells was able to enter a reversible nonproliferative state of drug tolerance. This subpopulation exhibited mesenchymal properties, NRF2 target gene expression, and sensitivity to ferroptotic cell death. Exploiting this induced collateral sensitivity by GPX4 inhibition clears drug-tolerant populations and leads to tumor cell eradication. Overall, this experimental in vitro data and theoretical modeling demonstrate why targeted mono- and dual therapies will likely fail in sufficiently large cancer cell populations to limit long-term efficacy. Our approach is not tied to a particular driver mechanism and can be used to systematically assess and ideally exhaust the resistance landscape for different cancer types to rationally design combination therapies. Significance: Unraveling the trajectories of preexisting resistant and drug-tolerant persister cells facilitates the rational design of multidrug combination or sequential therapies, presenting an approach to explore for treating EGFR-mutant lung cancer.