The principles that govern the evolution of tumors exposed to targeted therapy are poorly understood. Here we modeled the selection and propagation of an amplification in the BRAF oncogene (BRAFamp) in patient-derived tumor xenografts (PDXs) that were treated with a direct inhibitor of the kinase ERK, either alone or in combination with other ERK signaling inhibitors. Single-cell sequencing and multiplex fluorescence in situ hybridization analyses mapped the emergence of extra-chromosomal amplification in parallel evolutionary trajectories that arose in the same tumor shortly after treatment. The evolutionary selection of BRAFamp was determined by the fitness threshold, the barrier that subclonal populations need to overcome to regain fitness in the presence of therapy. This differed for inhibitors of ERK signaling, suggesting that sequential monotherapy is ineffective and selects for a progressively higher BRAF copy number. Concurrent targeting of the RAF, MEK and ERK kinases, however, imposed a sufficiently high fitness threshold to prevent the propagation of subclones with high-level BRAFamp. When administered on an intermittent schedule, this treatment inhibited tumor growth in 11/11 PDXs of lung cancer or melanoma without apparent toxicity in mice. Thus, gene amplification can be acquired and expanded through parallel evolution, enabling tumors to adapt while maintaining their intratumoral heterogeneity. Treatments that impose the highest fitness threshold will likely prevent the evolution of resistance-causing alterations and, thus, merit testing in patients.