A unified framework is developed to describe extrapolations from simulations performed in either a single system box or two subsystems at equilibrium (i.e., Gibbs ensembles). It is shown that the Gibbs ensemble can be used in conjunction with histogram reweighting and pseudo-ensemble techniques in order to map out more effectively different kinds of phase diagrams, in particular for binary and ternary systems. These extrapolation schemes allow the use of different phase-equilibrium specifications, some of which could not be simulated by conventional approaches. Novel semi-open and osmotic Gibbs ensembles are also described as counterparts of single-phase open and osmotic ensembles, respectively. Applications of the proposed methods are presented to the simulation of pressure-composition diagrams, bubble lines, and isoenthalpic partitioning.