This letter presents a generic coordination approach for the control of mobile manipulators. It is based on an external coupled coordination and exploits a multi-trajectory following approach. A coordination stage provides optimal offsets with respect to system sub-parts reference trajectories that minimize a cost function to manage the system redundancies. In order to face the diversity of tasks to be performed by the robotic platform, the cost function is composed of different criteria that can be adapted, pending on the mission assigned to the robot. A demonstration of its generic properties is proposed on different mobile manipulator structures in simulations. Finally, the effectiveness of the proposed method is evaluated through full-scale experiments with a single-arm skid steering mobile manipulator.