The molecular thermodynamic model of polymer solutions based on a close-packed lattice model presented in a previous work has been generally extended to multicomponent chainlike fluid mixtures. The Helmholtz function of mixing contains three terms, i.e., the contribution of athermal mixing of polymer chains, which is calculated by Guggenheim's theory; the contribution of nearest-neighbor interactions between monomers, which is calculated by Yang et al.'s model of the Helmholtz function of mixing for a multicomponent Ising lattice; and the contribution of the formation of polymer chains from monomers, which is obtained according C, to the sticky-point theory of Cummings, Zhou, and Stell. The liquid-liquid phase equilibria of ternary chainlike mixtures predicted by this model are in good agreement with Monte Carlo simulation results and superior to the results calculated by Flory-Huggins (FH) theory and revised Freed theory (RFT) obviously. This model not only can describe types 1-3 phase separations of Treybal classification satisfactorily, but can also correlate well the coexistence curves of binary polymer blends systems with an upper critical solution temperature (UCST) or a lower critical solution temperature (LCST). Meanwhile, model parameters correlated from the binary system can be further extended to predict the corresponding liquid-liquid equilibrium of ternary mixtures, including systems of ionic liquids.