Augmenting the physical strength of a human operator during unpredictable human-directed (volitional) movements is a relevant capability for several proposed exoskeleton applications, including mobility augmentation, manual material handling, and tool operation. Unlike controllers and augmentation systems designed for repetitive tasks (e.g., walking), we approach physical strength augmentation by a task-agnostic method of force amplification—using force/torque sensors at the human–machine interface to estimate the human task force, and then amplifying it with the exoskeleton. We deploy an amplification controller that is integrated into a complete whole-body control framework for controlling exoskeletons that includes human-led foot transitions, inequality constraints, and a computationally efficient prioritization. A powered lower-body exoskeleton is used to demonstrate behavior of the control framework in a lab environment. This exoskeleton can assist the operator in lifting an unknown backpack payload while remaining fully backdrivable.