Membraneless organelles are phase-separated droplets that are dynamically assembled and dissolved in response to biochemical reactions in cells. Complex coacervate droplets produced by associative liquid-liquid phase separation offer a promising approach to mimic such dynamic compartmentalization. Here, we present a model for membraneless organelles based on enzyme/polyelectrolyte complex coacervates able to induce their own condensation and dissolution. We show that glucose oxidase forms coacervate droplets with a cationic polysaccharide on a narrow pH range, so that enzyme-driven monotonic pH changes regulate the emergence, growth, decay and dissolution of the droplets depending on the substrate concentration. Significantly, we demonstrate that time-programmed coacervate assembly and dissolution can be achieved in a single-enzyme system. We further exploit this self-driven enzyme phase separation to produce multiphase droplets via dynamic polyion self-sorting in the presence of a secondary coacervate phase. Taken together, our results open perspectives for the realization of programmable synthetic membraneless organelles based on self-regulated enzyme/polyelectrolyte complex coacervation.