Self-assembly is a powerful paradigm, wherein molecules spontaneously form ordered phases exhibiting well-defined nanoscale periodicity and shapes. However, the inherent energy-minimization aspect of self-assembly yields a very limited set of morphologies, such as lamellae or hexagonally packed cylinders. Here, we show how soft self-assembling materials—block copolymer thin films—can be manipulated to form a diverse library of previously unreported morphologies. In this iterative assembly process, each polymer layer acts as both a structural component of the final morphology and a template for directing the order of subsequent layers. Specifically, block copolymer films are immobilized on surfaces, and template successive layers through subtle surface topography. This strategy generates an enormous variety of three-dimensional morphologies that are absent in the native block copolymer phase diagram.