The Integrated Quadratic Solvation Relationship (IQSR) method is studied with respect to its applicability to three main classes of quaternary liquid-liquid equilibrium systems in combination with their ternary subsystems. We utilize multilinear methodology with a wide range of numerical simulation scenarios to generate an appropriate quadratic functionality of six physical indices combined with the boundary constraints of relevant systems. The IQSR method is applied to the estimation of four newly-proposed extraction factors to demonstrate its attractive application. By building-up three general hybrid forms including twelve adjustable coefficients we are able to validate the examined multilinear technique against the equilibrium data that span total 52 literature liquid-liquid systems being subjected to statistical analysis. It is concluded that the IQSR method offers mathematical reliability due to its robustness, initialization/parameterization-free nature and ease of hybridization with standard Gibbs energy model so long as solvent effects are concerned. (C) 2018 Elsevier B.V. All rights reserved.