The principles governing evolution of tumors exposed to targeted therapy are poorly understood. Here we modeled the selection and propagation of BRAF amplification ( BRAF amp) in patient-derived tumor xenografts (PDX) treated with a direct ERK inhibitor, alone or in combination with other pathway inhibitors. Single cell sequencing and multiplex-fluorescence in situ hybridization mapped the emergence of extra-chromosomal amplification in parallel evolutionary tracts, arising in the same tumor shortly after treatment. The evolutionary selection of BRAF amp is determined by the fitness threshold, the barrier subclonal populations need to overcome to regain fitness in the presence of therapy. This differed for ERK signaling inhibitors, suggesting that sequential monotherapy is ineffective and selects for a progressively higher BRAF copy number. Concurrent targeting of RAF, MEK and ERK, however, imposes a sufficiently high fitness threshold to prevent the propagation of subclones with high-level amplification. Administered on an intermittent schedule, this treatment inhibited tumor growth in 11/11-lung cancer and melanoma PDX 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 merit testing in patients.