Interactions of Ag and Sb(III) and Sn(IV) sulfides were investigated by x-ray diffraction, differential thermal analysis and microstructure analysis methods. The quaternary compound Ag11Sb3SnS12 was found for the first time in the Ag2S-Sb2S3-SnS2 system at 500 K (227 °C) at the intersection of AgSbS2-Ag8SnS6 and Ag3SbS3-Ag2SnS3. The compound melts congruently at 920 K (647 °C) and has a polymorphous transition at 646 K (373 °C). The quasi-ternary system is characterized by solid solution ranges of the binary compounds Ag2S, Sb2S3, SnS2, ternary Ag3SbS3, AgSbS2, Ag8SnS6, Ag2SnS3 and quaternary compound Ag11Sb3SnS12. The separation of the composition triangle into 10 single-phase, 18 two-phase, and 9 three-phase fields was established. Seven vertical sections were investigated of which five are quasi-binary (Ag3SbS3-Ag8SnS6, Ag3SbS3-Ag2SnS3, AgSbS2-Ag8SnS6, AgSbS2-Ag2SnS3, AgSbS2-SnS2). The AgSbS2-Ag4Sn3S8 and AgSbS2-Sb2SnS5 sections are non-quasi-binary due to peritectic formation of Ag4Sn3S8 and Sb2SnS5. The liquidus surface projection of the Ag2S-Sb2S3-SnS2 system consists of 10 fields of primary crystallization of the solid solutions α-Ag2S, β-Sb2S3, γ-SnS2, δ-Ag3SbS3, ε′-AgSbS2, ζ-Ag8SnS6, η-Ag2SnS3, σ-Ag11Sb3SnS12 and compounds Ag4Sn3S8 and Sb2SnS5. These are separated by curves of monovariant equilibria that converge at 9 ternary invariant points (7 eutectic (E1-E7) and 2 quasi-peritectic (U1, U2)).