Time-Optimal Path Parameterization (TOPP) under ac-tuation bounds plays a fundamental role in many robotic theories and applications. This algorithm was first developed and perfected for classical serial robotic manipulators whose actuation is non-redundant. Yet, redundantly-actuated systems, such as parallel manipulators or humanoid robots in multi-contact tasks, are increasingly common in all fields of robotics. Here we extend the classical algorithm of TOPP (a.k.a. numerical integration approach) to the case of redundantly-actuated systems. As illustration, we present an application to multi-contact trajectory planning for a humanoid robot.