A recently developed formalism that synthesizes the description of statistical mechanical ensembles and the extrapolation of simulation data thereof is extended to encompass the formulation of semigrand canonical (SGC) type of ensembles and of ensembles suitable for confined systems and reactive equilibrium. These extensions provide a convenient framework to cast several ensembles previously used and also to formulate new variants. The advocated framework and its associated notation system are used to give general relationships for performing Monte Carlo simulations (acceptance rules) and implementing extrapolation and perturbation calculations. It is also shown how extrapolation methods can be systematically used to target equilibrium states whose specification does not allow the use of a direct simulation approach.