Members of the mitogen-activated protein kinase (MAPK) pathway are commonly mutated in cancer due to the important role of the pathway in regulating proliferation and survival. Mutations in KRAS and BRAF account for the majority of cases, and are often found in melanoma, lung, and colorectal cancers. Intense efforts have led to the development of many small molecule inhibitors that target this pathway. While many of these inhibitors have shown clinical efficacy, they are susceptible to adaptation by tumors cells that ultimately lead to drug resistance. Here we studied tumor adaptation mechanisms to two novel inhibitors targeting members of this pathway using single cell sequencing techniques, and identified strategies to prevent them. First, using shallow whole genome single-cell DNA sequencing, we found that BRAF amplification can rapidly emerge through multiple evolutionary paths in BRAFV600E-mutant cancer cells treated with an ERK inhibitor. BRAF amplification can cause resistance to RAF, MEK and ERK inhibitors, but the selective pressure imposed by each drug differs and sequential therapy likely selects for progressively higher BRAF copy number. An intermittent triple therapy composed of RAF/MEK/ERK inhibitors has potent antitumor activity and imposes a sufficiently high selective pressure to suppress the emergence of BRAF amplification. Second, we evaluated how KRASG12C-mutant lung cancer respond to the novel KRASG12C conformation specific inhibitor. Using single cell RNA sequencing, we found that shortly after treatment, while the majority of cells were inhibited, others adapted rapidly by restoring KRAS transcriptional output. This divergent response is due to upregulation of KRAS transcription and expression in some cells in response to suppressed MAPK pathway output. Along with reactivation of upstream adaptive signals such as EGFR signaling, this new KRAS protein is more likely to be in a drug insensitive state. Combination therapies that suppress the induction of KRASG12C protein, or those that prevent its conversion to the active state, should enhance the potency and duration of inhibition.