Systems-of-systems are formed by the composition of independently created software components. These components are designed to satisfy their individual requirements, rather than the global requirements of the systems-of-systems. We refer to components that cannot be adapted to meet both individual and global requirements as defiant components. In this paper, we propose a cautious adaptation approach which supports changing the behaviour of such defiant components under exceptional conditions to satisfy global requirements, while continuing to guarantee the satisfaction of the components’ individual requirements. The approach represents both normal and exceptional conditions as scenarios; models the behaviour of exceptional conditions as wrappers implemented using an aspect-oriented technique; and deals with both single and multiple instances of defiant components with different precedence order at runtime. We evaluated an implementation of the approach using drones and boats for an organ delivery application conceived by our industrial partners, in which we assess how the proposed approach helps achieve the system-of-systems’ global requirements while accommodating increased complexity of hybrid aspects such as multiplicity, precedence ordering, openness, and heterogeneity.