It is known that a closed-loop dynamical system subject to an adaptive controller remains stable either if there does not exist significant unmodelled dynamics or the effect of system uncertainties is negligible. This implies that these controllers cannot tolerate large system uncertainties even when the unmodelled dynamics satisfy a set of conditions. In this paper, we present an adaptive control architecture such that the proposed adaptive controller is augmented with an adaptive robustifying term. Unlike standard adaptive controllers, the proposed architecture allows the closed-loop dynamical system to remain stable in the presence of large system uncertainties when the unmodelled system dynamics satisfy a set of conditions. A numerical example is provided to demonstrate the efficacy of the proposed approach.