We clarified the phase behavior of a mixture of water, an alkane, a nonionic amphiphile, and a fluorinated alkane. Of the four ternary mixtures, three separate into three coexisting liquid phases within a certain temperature interval, while the fourth separates into three phases inside the phase tetrahedron. As a consequence, the quaternary mixture separates into four liquid phases, namely, an amphiphile-rich phase coexisting with one water-rich and two oil-rich phases. The four-phase body exists within a temperature interval that is determined by the highest one of the lower and the lowest one of the upper critical tie-lines of the four three-phase bodies. The results may serve as the basis for preparing microemulsions with two incompletely miscible organic liquids.