The Debenedetti-Kumar (DK) formula for solute fugacity coefficients in highly dilute binary solutions has been generalized to multicomponent mixtures with a single solvent and several solutes at high dilution. It is shown how models based on conformal solution (CS) theory or the Kirkwood-Buff (KB) solution theory or their combination may be used to investigate the cosolute effect on the solubilities of solids in supercritical (SC) fluid solvents. The generalized DK (GDK) formulae have been tested with the Peng-Robinson (PR) equation of state (EOS), by using it to compute approximate solute fugacity coefficients in dilute ternary SC solutions with two solids (solute and cosolute) at various dilutions and comparing with values based on the use of exact thermodynamic expressions with the PR EOS for fugacity coefficients in mixtures. The two sets of values are found to be in good agreement. Further tests along these lines consist of using both sets of solute fugacity coefficients in standard phase equilibrium equations to evaluate solute and cosolute mole fractions. Again, the two sets of values determined in this way show good agreement, thereby giving us grounds to suppose the GDK formulae are of sufficient accuracy to be used in the study of such mixtures. The CS model has been used in conjunction with the GDK formulae to successfully correlate several solid solubilities in SC CO, in the presence of a cosolute. Other potential applications of the GDK formulae include modeling the solubility of gases in liquids and the solubility of solids in SC fluid solvents containing an added entrainer.