By building on the Advanced Distillation Curve (ADC) approach to measuring the volatility of fuels and other fluid mixtures, the ADC with Reflux or ADCR technique was developed to address the difficulty of experimentally determining the vapor-liquid equilibrium of fluids containing many components. For fuels and other multicomponent mixtures, the ADCR collects data about the chemical compositions of both liquid and vapor phases across a range of temperatures, elucidating the two-phase region at constant pressure. Two simple mixtures were used to demonstrate the ADCR method: an n-decane/n-tetradecane binary and the Huber-Bruno surrogate, a ternary mixture designed to represent the volatility of an aviation turbine kerosene. These mixtures were chosen to test the method because they have been extensively studied and modeled in previous work. For both test fluids, the ADCR measurements of vapor-liquid equilibrium were in good agreement with model predictions. We conclude that the ADCR is a useful method for determining the T-P-x-y behavior of fluid mixtures with many components. The experimental approach presented may support the development of fuels, design of separations, and forensic sciences that use vapor analysis, especially arson fire debris analysis, by providing quantitative data with well-characterized uncertainty describing the relationships between the vapor and condensed phases of a fuel subjected to thermal weathering.