The solubility in triple water-salt systems containing NdCl3, PrCl3, YCl3, TbCl3 chlorides, and water-soluble fullerenol C60(OH)24 at 25 °C was studied by isothermal saturation in ampoules. The analysis for the content of rare earth elements was carried out by atomic absorption spectroscopy, for the content of fullerenol—by electronic spectrophotometry. The solubility diagrams in all four ternary systems are simple eutonic, both consisting of two branches, corresponding to the crystallization of fullerenol crystal-hydrate and rare earth chloride crystal-hydrates, and containing one nonvariant point corresponding to the saturation of both solid phases. On the long branches of C60(OH)24*18H2O crystallization, a C60(OH)24 decreases by more than 2 orders of magnitude compared to the solubility of fullerenol in pure water (salting-out effect). On very short branches of crystallization of NdCl3*6H2O, PrCl3*7H2O, YCl3*6H2O, and TbCl3*6H2O, the salting-in effect is clearly observed, and the solubility of all four chlorides increases markedly. The four diagrams cannot be correctly approximated by the simple one-term Sechenov equation (SE-1), and very accurately approximated by the three-term modified Sechenov equation (SEM-3). Both equations for the calculation of nonelectrolyte solubility in electrolyte solutions (SE-1 and SEM-3 models) are obtained, using Pitzer model of virial decomposition of excess Gibbs energy of electrolyte solution. It is shown, that semi-empirical equations of SE-1 and SEM-3 models may be extended to the systems with crystallization of crystal-solvates.