Sequential composition is an effective supervisory control method for addressing control problems in nonlinear dynamical systems. It executes a set of controllers sequentially to achieve a control specification that cannot be realized by a single controller. As these controllers are designed offline, sequential composition cannot address unmodeled situations that might occur during runtime. This paper proposes a learning approach to augment the standard sequential composition framework by using online learning to handle unforeseen situations. New controllers are acquired via learning and added to the existing supervisory control structure. In the proposed setting, learning experiments are restricted to take place within the domain of attraction (DOA) of the existing controllers. This guarantees that the learning process is safe (i.e., the closed loop system is always stable). In addition, the DOA of the new learned controller is approximated after each learning trial. This keeps the learning process short as learning is terminated as soon as the DOA of the learned controller is sufficiently large. The proposed approach has been implemented on two nonlinear systems: 1) a nonlinear mass-damper system and 2) an inverted pendulum. The results show that in both cases a new controller can be rapidly learned and added to the supervisory control structure.