Previous work has emphasized that cognitive functions in the human brain are organized into large-scale networks. However, the mechanisms that allow these networks to compensate for focal disruptions remain elusive. I suggest a new perspective on the compensatory flexibility of cognitive networks. First, I demonstrate that cognitive networks can rapidly change the functional weight of the relative contribution of different regions. Second, I argue that there is an asymmetry in the compensatory potential of different kinds of networks. Specifically, recruitment of domain-general functions can partially compensate for focal disruptions of specialized cognitive functions, but not vice versa. Considering the compensatory potential within and across networks will increase our understanding of functional adaptation and reorganization after brain lesions and offers a new perspective on large-scale neural network (re-)organization.