As a test for our method, we have tackled the Li-P-S-Cl space where only 16 stable (68 metastable crystals) are present in the Materials Project. Stable crystalline phases are well established for binary compounds at the edges of the phase diagram such as Li3P, LiCl and Li2S. Using our approach, 17 new stable structures are proposed below the convex hull, along with 435 metastable structures.