Topological quantum computing requires phases of matter which host fractionalized excitations that are neither bosons nor fermions. I will present a new route toward realizing such fractionalized phases of matter by literally building on existing topological phases. I will first discuss how existing topological phases, when interfaced with other systems, can exhibit a “topological proximity effect” in which nontrivial topology of a different nature is induced in the neighboring system. Then, I will show how this enables a new entanglement based technique (the “topological bootstrap”) for upgrading topological phases from the integer into the fractional quantum Hall variety. Finally, I will highlight the rich phenomenology of systems with interacting Majorana modes. Such systems can exhibit physics ranging from black hole scrambling to supersymmetry and from alternative surface code architectures to topological phases in three dimensions with completely immobile excitations. I will discuss my plans for understanding both general properties and specific models of such fascinating systems.