Phase diagrams of boundary quasi-binary systems within the composition triangle of the Bi2S3‒Bi2Se3‒BiI3 system (A) were investigated for selected compositions based on a limited number of DTA data and the solid-phase equilibrium diagram of system (A). Analytical equations were derived for the liquidus curves of phases in the boundary systems, as well as for the liquidus surfaces of solid solutions based on Bi2S3, Bi2Se3 compounds in system (A), and for the intermediate phases BiS1-xSexI and Bi19S27(1-x)Se27xI3. Based on the obtained equations, a 3D visualization of the liquidus surface of system (A) was performed, and the types and coordinates of mono- and nonvariant equilibria present in the system were determined. Using the constructed 3D model of the liquidus surface, several isopleth sections of the T–x–y phase diagram were developed and validated by DTA results obtained from a limited number of samples. The presented results can be applied to the synthesis and crystal growth of BiS1-xSexI and Bi19S27(1-x)Se27xI3 solid solutions with tunable composition and properties.