Excess-sulfate phosphogypsum slag grouting material (EPSGM) has strong advantages for stabilizing the coral sand foundation, which requires establishing a groutability prediction model involving multi-factors to ensure better stabilization. Specifically, the grain size (d85) and water-to-cement ratio (w/c) of the grout, particle size (D15), relative density (Dr), and fine content (FC) of coral sand, and grouting pressure (P) are considered. The results show that the optimal particle size d85 of EPSGM is 15.567 μm. As the w/c increases from 1.0 to 3.0, the compressive strength of mortar (EPSGM + coral sand) decreases from 11.74 MPa to 0.32 MPa, and the California Bearing Ratio (CBR) value meets the typical requirements (≥ 15%). The groutability criterion (N) is positively correlated with the D15, w/c, and P, while it is negatively correlated with the Dr and FC, namely, the model writes: N=1−0.071Dr1−1.54FC0.024D15d85+0.42w/c+0.897P−0.86. Particularly, the predictive accuracy can attain a level of 87.50% for systems characterized by varying grain sizes (D15 ≥ 0.431 mm) and densities (Dr ≤ 0.67) of EPSGM stabilizing coral sand foundations. Furthermore, it also applies to other systems in literature that exhibit accuracy ranging from 33.33% to 62.50%. Therefore, the derived predictive model performs greater engineering relevance in informing the selection of grout factors.