Oesophageal squamous cell carcinoma is a deadly disease where systemic therapy has relied upon empiric chemotherapy despite the presence of genomic alterations pointing to candidate therapeutic targets, including recurrent amplification of the gene encoding receptor tyrosine kinase epidermal growth factor receptor (EGFR). Here, we demonstrate that EGFR-targeting small-molecule inhibitors have efficacy in EGFR-amplified oesophageal squamous cell carcinoma (ESCC), but may become quickly ineffective. Resistance can occur following the emergence of epithelial-mesenchymal transition and by reactivation of the mitogen-activated protein kinase (MAPK) pathway following EGFR blockade. We demonstrate that blockade of this rebound activation with MEK (mitogen-activated protein kinase kinase) inhibition enhances EGFR inhibitor-induced apoptosis and cell cycle arrest, and delays resistance to EGFR monotherapy. Furthermore, genomic profiling shows that cell cycle regulators are altered in the majority of EGFR-amplified tumours and a combination of cyclin-dependent kinase 4/6 (CDK4/6) and EGFR inhibitors prevents the emergence of resistance in vitro and in vivo. These data suggest that upfront combination strategies targeting EGFR amplification, guided by adaptive pathway reactivation or by co-occurring genomic alterations, should be tested clinically.