Sequential composition is a supervisory control architecture for addressing control problems in complex dynamical systems. Although sequential composition works properly for a single system, it is not designed for cooperative systems. This paper extends the standard sequential composition by introducing a novel approach to compose multiple sequential composition controllers towards cooperative control. Given two or more systems, cooperation is achieved by composing each of the systems' control automaton, together with estimation for the domains of attraction of the resulting composed controllers. This typically results in new events for the original sequential composition controllers. Applying these events, the cooperative control system can fulfill the tasks which are not possible to satisfy with the original controllers individually. The simulation results of an inverted pendulum system collaborating with two second-order DC motors are presented for cooperative swing-up maneuvers.