Compensatory mechanisms, such as relief of AKT-ErbB3-negative feedback, are known to desensitize ErbB2-dependent tumours to targeted therapy. Here we describe an adaptation mechanism leading to reactivation of the PI3K/AKT pathway during trastuzumab treatment, which occurs independently of ErbB3 re-phosphorylation. This signalling bypass of phospho-ErbB3 operates in ErbB2-overexpressing cells via RAS-PI3K crosstalk and is attributable to active ErbB2 homodimers. As demonstrated by dual blockade of ErbB2/RAS and ErbB3 by means of pharmacological inhibition, RNA interference or by specific protein binders obstructing the RAS-p110α interaction, both routes must be blocked to prevent reactivation of the PI3K/AKT pathway. Applying these general principles, we developed biparatopic designed ankyrin repeat proteins (DARPins) trapping ErbB2 in a dimerization-incompetent state, which entail pan-ErbB inhibition and a permanent OFF state in the oncogenic signalling, thereby triggering extensive apoptosis in ErbB2-addicted tumours. Thus, these novel insights into mechanisms underlying network robustness provide a guide for overcoming adaptation response to ErbB2/ErbB3-targeted therapy.