Accurate estimates of the binary, ternary, and quaternary interactions in aqueous ionic mixtures with uncommon ions with hydrophobic character are presented. For this purpose, the values of the excess Gibbs free energy of mixing, Delta(m)G(E), obtained from our earlier isopiestic osmotic coefficients (Kumar, A. J. Phys. Chem. B 2003. 107, 2808) for the mixtures of NaCl with four guanidinium (Gn(+)) salts-CH(3)COOGn, GnNO(3), GnClO(4), and Gn(2)SO(4) are analyzed with the help of the method developed by Leifer and Wigent. The methodology of Leifer and Wigent is based on the equations of Scatchard-Rush-Johnson and Friedman's cluster integral expansion theory. The Scatchard-Rush-Johnson theory explicitly considers the quaternary and higher-order ionic interactions in the mixtures as compared to the specific ion interaction theory of Pitzer, which accounts for binary and ternary interactions only. The contributions due to binary, ternary, and quaternary interaction terms to total Delta(m)G(E) are estimated and discussed critically. Also, the interaction between the same two cations, for example, Gn(+)-Gn(+), is estimated and found significant, which otherwise cannot be obtained by the use of Pitzer's theory. The information obtained from the analysis of Delta(m)G(E) is also supported by the newly measured excess volumes of mixing, Delta(m)V(E), at 298.15 K. The individual contributions of the binary, ternary, and quaternary interaction terms to total Delta(m)V(E) are described. The binary, ternary, and quaternary interaction terms for both Delta(m)G(E) and Delta(m)V(E) are analyzed in terms of Friedman's cluster integral expansion theory.