An asymptotic analysis based on Taylor series expansions is used for first-order correction terms to the Henry's law approximation to describe solvation phenomena in multiple solute-multiple solvent systems. The magnitude of these correction terms in solvent systems very near their critical points is of particular concern, as shown in model fluid calculations with the aid of integral equation theory. The results clearly demonstrate that close proximity to the critical point in pure and mixed solvent systems causes the Henry's law approximation to show large errors in predicting solubilities, especially near the critical azeotrope of a mixed solvent system. Theoretical results also show that cross solubility enhancements in a two solutesupercritical solvent system cause cooperative synergism (both solute solubilities are increased relative to the corresponding single solute situations) or reverse synergism (both depressed relative to the single solute situation). It appears to be consistent with the available data. In computer simulations, the solute's infinitely dilute reference state is often used as a basis for describing solute thermodynamic behavior. These simulations are best achieved in the canonical ensemble because of the weak composition dependence of free energies in terms of characteristic variables of this ensemble.