We investigate the problem of designing an adaptive performance enhancement control law for an arbitrarily fast switching linear plant given a switching compensator. Switching is assumed to be uncontrolled and the characteristics of the reference or disturbance signals are changing over time. Stability despite switching and adaptation are given by construction, using a parameterization of all quadratically stabilizing compensators. We show that the adaptive-Q control methodology is well suited to enhance performance online for the switching linear case. A simulation example of an unstable switching plant illustrates the efficacy of the method and the performance enhancement when tracking a bounded reference signal with unknown characteristics.