In this work, we examine, using molecular simulation, the liquid-vapor phase equilibria and atomic-level structure of an ethylene-expanded mixture of methanol, water and hydrogen peroxide as functions of temperature and pressure. The motivation for this study is a recently proposed catalytic process for the epoxidation of ethylene to ethylene oxide in Nb-doped silica nanopores [J. Catal. 336 75 (2016)], where the solvent (methanol) is expanded by the reactant (ethylene) in the presence of the oxidant (hydrogen peroxide in water). Optimal tuning of the reaction conditions can be greatly facilitated by detailed information as to the phase equilibrium and local structure (e.g., hydrogen bonding) of this quaternary mixture. In particular, we focus on the solubility of ethylene in this system as a function of water content. We compare this quaternary system to the recently studied ethylene/methanol/water ternary mixture [Fluid Phase Equilib. 429 275 (2016)]. One major conclusion of this work is that for solutions in which the methanol to water/hydrogen peroxide ratio is greater than 50%, the solubility of ethylene in the quaternary mixture is identical within the statistical error to that of a corresponding ternary mixture, in which hydrogen peroxide is replaced by water. Given that these methanol-rich systems are precisely those of most utility in the epoxidation process, this observation greatly simplifies the phase-equilibrium analysis.