Solid-liquid-liquid-vapor (SLLV) phase behavior is the most complex phase behavior anticipated in the phase diagrams for reservoir fluids and heavy oils and is therefore the kernel to understanding the phase diagrams for such systems. As a first step toward modeling the phase behavior of such complex fluids, a method for predicting SL1L2V phase behavior in binary, ternary and quaternary synthetic mixtures is presented. The method is based on standard K- and L-point computation routines and a semi-empirical average solubility model (regressed with 22 binary SLLV data points) which defines the intersection of LLV phase behavior with SLV phase behavior. Predicted SLLV phase behavior results for an additional 16 binary, and related ternary and quaternary systems are presented. Limits for SLLV phase behavior for specific solvent + solute 'families' are discussed. The results clearly show the roles played by solvent constituents and critical phenomena and help explain the comparative rarity of this phase behavior in multi-component mixtures. The results also highlight the need to custom regress interaction parameters so that the known phase behavior types of binary mixtures are reproduced by equations of state. (C) 2003 Elsevier Science B.V. All rights reserved.