Solid-vapor phase equilibria describe the volatile ices on Pluto’s surface (Tan & Kargel 2018, MNRAS 474, 4254). A simple model of the atmosphere with three components N₂/CH₄/CO may have solved the long-standing puzzle of the existence of CH₄-rich ice in addition to the expected N₂-rich ice. An isobaric treatment using CRYOCHEM equation of state naturally results in one solid phase of either ice, which is in equilibrium with the atmosphere, depending on the local temperature variations of Pluto’s surface. CH₄-rich ice forms at higher temperatures, while N₂-rich ice forms at lower temperatures. A temperature also exists on Pluto where three phases coexist, including vapor in equilibrium with two ices, and where the ices can switch from one type to the other upon cooling or warming. Our model relies on fundamental physics-based thermodynamics, and it explains New Horizons observations of the distributions of these ices, as presented by Bertrand et al. (Nat. Commun. 2020, 11, 1), without invoking a vertically distributed atmospheric CH₄ that has not been verified with observation. As observed by New Horizons, Pluto’s surface has valley networks and channels, perhaps resulting from either fluvial (Moore et al. 2016, Science 351, 1284) or glacial (Howard et al. 2017, Icarus 287, 287; Umurhan et al. 2017, Icarus 287, 301) mechanisms, or both, at the present or in the past. Considering the present freezing condition on the surface, if the mechanisms are still in action, they must occur under the surface. Therefore, it is of great interest to know the phase equilibria involving the ices and liquid at conditions that may exist underground. Similar to the treatment of the surface ices, this work also applies CRYOCHEM to describe the phase equilibria that progress through depth as the temperature and pressure increase. The fate of the ices can be determined by examining the resulting phase diagrams at conditions at different depths, specifically the appearance of a liquid phase.