A combined machine learning approach and first-principles calculations are employed to efficiently explore energetically favorable ternary compounds involving Pt and an immiscible Si-Sn pair of elements. We predict two stable Pt-Si-Sn ternary compounds (Pt2Si2Sn and Pt8SiSn2) and reproduce the experimentally synthesized Pt5SiSn. The crystal structures of Pt5SiSn and Pt8SiSn2 are composed of a SiPt8 cube and SnPt12 cuboctahedron. Based on these structural motifs, we design a series of Pt-Si-Sn ternary compounds that contain SiPt8 and SnPt12 units and discover some stable and metastable compounds. Partial flat bands near the Fermi level appear in these compounds, and the positions of partial flat bands move upward with increasing the Pt content. The partial flat bands are dominated by Pt atoms. These Pt-Si-Sn ternary compounds provide a platform to study flat band-related properties. Our results open a way to design new compounds in the ternary system.