Hypothesis: Various advanced geometries are endowed by the unique structure of "three rooms" of immiscible oils composing the Cerberus droplets. Adjustable interfacial properties and tunable volume ratio in the four-liquid system render it possible to realize the controlled morphology transition by the variation of temperature and emulsion composition. Experiments: Cerberus emulsions are prepared in batch scale by traditional one-step vortex mixing, employing the oil combinations of methacryloxypropyl dimethyl silicone (DMS)/2-(perfluorooctyl) ethyl methacrylate (PFOEMA)/vegetable oil (VO). Emulsifier of pluoronic F127, a temperature sensitive surfactant is applied. Stereoscopic topological phase diagram as functions of temperature and composition are plotted. Numerical calculations on the droplet morphology including interface curvature, contact angle, and volume fraction of each domain are performed. Findings: Four primary regions with specific morphologies, i.e. "VO > DMS < PFOEMA", "VO > DMS > PFOEMA", "VO < DMS > PFOEMA", and finally "VO < DMS < PFOEMA" are obtained. Extended volume ratio range of three lobes, from about 0.03 to 23.3, is achieved and precisely controlled based on the three-phase diagram. What is more, the structural features are found to be thermodynamically determined by the minimization of interfacial energy, though the emulsion is prepared kinetically by vortex mixing. The findings are attractive in the fields of materials synthesis and microreactors. (C) 2019 Elsevier Inc. All rights reserved.