In this work we report phase equilibrium measurements on the system (methane + carbon dioxide + water) carried out with a high-pressure quasi-static-analytical apparatus. The measurements have been made under conditions of two-phase vapor-liquid equilibrium, three-phase vapor-liquid-liquid equilibrium (VLLE), and four-phase vapor-liquid-liquid-hydrate equilibrium. The compositions of three coexisting fluid phases have been obtained along eight isotherms at temperatures from (285.15 to 303.5) K and at pressures up to either the upper critical end point (UCEP) or up to the hydrate formation locus. Compositions of coexisting vapor and liquid phases have been obtained along three isotherms at temperatures from (323.15 to 423.15) K and pressures up to 20 MPa. The quadruple curve, along which hydrates coexist with the three fluid phases, was also measured along its entire length. The VLLE data obtained for this mixture have been compared with the predictions of the statistical associating fluid theory for potentials of variable range (SAFT-VR), implemented with the square-well potential and using parameters fitted to pure-component and binary-mixture data. Specifically, we used the SAFT-VR parameters reported by Mı́guez and co-workers [Mı́guez, J. M.; dos Ramos, M. C.; Piñeiro, M. M.; Blas, F. J. J. Phys. Chem. B 2011, 115, 9604]. The pressure along the quadruple curve was compared with the predictions of two different thermodynamic models. Furthermore, a detailed study of the ternary mixtures was carried out based on comparison with available ternary data of the type (CO2 + n-alkane + water) and available data for the constituent binary subsystems. In this way, we analyzed the observed effects on the solubility when the n-alkane component was changed or a third component was added.