The competition between crystallization and oiling-out is a major concern in the process design of antisolvent crystallization for poorly water-soluble drugs. Within the CALPHAD framework, this study demonstrates the extrapolation of the ternary phase diagram for antisolvent crystallization from the solubility data, resorting to the Jouyban-Acree model and the Gibbs-Helmholtz type equation. The ternary phase diagram for DBDCS (a fluorophore exhibiting aggregation-induced emission) in water-[1,4-dioxane] is constructed by calculating the polymorph solid-liquid equilibria, the metastable liquid-liquid equilibrium, and the spinodal limit. Our computational results agree with the phase diagram measured through microfluidics. By analyzing the chemical potential, we show that the solute uphill diffusion relies on the antisolvent gradient. The energy of disorder upon nucleation is found to be much smaller compared to the solute energy gain upon antisolvent addition. The characteristics of the parallel solubility curves of the polymorphs are explained with the analysis of the molecular interactions. By evaluating the energy of composition fluctuation, we suggest the optimal conditions for antisolvent crystallization. The insights obtained from this study can be extended to the process design of antisolvent crystallization for similar systems, and form the basis for further kinetic analysis of the competition between oiling-out and crystallization.