Epidermal growth factor receptor (EGFR) mutations identify patients with lung cancer who derive benefit from kinase inhibitors. However, most patients eventually develop resistance, primarily due to the T790M second‐site mutation. Irreversible inhibitors (e.g., osimertinib/AZD9291) inhibit T790M‐EGFR, but several mechanisms, including a third‐site mutation, C797S, confer renewed resistance. We previously reported that a triple mixture of monoclonal antibodies, 3×mAbs, simultaneously targeting EGFR, HER2, and HER3, inhibits T790M‐expressing tumors. We now report that 3×mAbs, including a triplet containing cetuximab and trastuzumab, inhibits C797S‐expressing tumors. Unlike osimertinib, which induces apoptosis, 3×mAbs promotes degradation of the three receptors and induces cellular senescence. Consistent with distinct mechanisms, treatments combining 3×mAbs plus sub‐inhibitory doses of osimertinib synergistically and persistently eliminated tumors. Thus, oligoclonal antibodies, either alone or in combination with kinase inhibitors, might preempt repeated cycles of treatment and rapid emergence of resistance.