We present Compositional 3D Printing, recasting the 3D printer as a tool for expression that responds to real-time design decisions, analogous to composing a piece of music using a mixer. Our paradigm supports a wide range of inputs and interactions for designers, to be used in the moment; not only before printing, but anytime during production. We propose the design space of this digital fabrication paradigm, and outline methods and technical details with which researchers and practitioners can expand this space.