The emergence of robot-based body augmentation promises exciting innovations that will inform robotics, human-machine interaction, and wearable electronics. Even though augmentative devices like extra robotic arms and fingers in many ways build on restorative technologies, they introduce unique challenges for bidirectional human-machine collaboration. Can humans adapt and learn to operate a new limb collaboratively with their biological limbs without sacrificing their physical abilities? To successfully achieve robotic body augmentation, we need to ensure that by giving a person an additional (artificial) limb, we are not in fact trading off an existing (biological) one. In this manuscript, we introduce the "Neural Resource Allocation" problem, which distinguishes body augmentation from existing robotics paradigms such as teleoperation and prosthetics. We discuss how to allow the effective and effortless voluntary control of augmentative devices without compromising the voluntary control of the biological body. In reviewing the relevant literature on extra robotic fingers and limbs we critically assess the range of potential solutions available for the "Neural Resource Allocation" problem. For this purpose, we combine multiple perspectives from engineering and neuroscience with considerations from human-machine interaction, sensory-motor integration, ethics and law. Altogether we aim to define common foundations and operating principles for the successful implementation of motor augmentation.