Humans and many animals exhibit a robust capability to manipulate diverse objects, often directly with their bodies and sometimes indirectly with tools. Such flexibility is likely enabled by the fundamental consistency in underlying physics of object manipulation such as contacts and force closures. Inspired by viewing tools as extensions of our bodies, we present Tool-As-Embodiment (TAE), a parameterization for tool-based manipulation policies that treat hand-object and tool-object interactions in the same representation space. The result is a single policy that can be applied recursively on robots to use end effectors to manipulate objects, and use objects as tools, i.e. new end-effectors, to manipulate other objects. By sharing experiences across different embodiments for grasping or pushing, our policy exhibits higher performance than if separate policies were trained. Our framework could utilize all experiences from different resolutions of tool-enabled embodiments to a single generic policy for each manipulation skill. Videos at https://sites.google.com/view/recursivemanipulation