Living systems continue to outstrip the most adaptive state-of-the-art AI and robotics. One reason for this is that, without exception, organisms and species constantly restructure themselves at all organizational levels, from the microsecond- to millennial time scales; most machines do not. Almost all AI and robots incorporate change at just one time scale – that of synaptic plasticity – and in one modality: neural networks. We thus propose to study embodied plasticity: how multi-level change supports intelligence in protean systems (cells, organs, organisms, and ecologies), and how best to channel those discoveries into protean machines (robots and artificial biological constructs) and algorithms (machine learning methods).