Pseudobinary phases (SnSe)(x)Bi2Se3 exhibit a very diverse structural chemistry characterized by different building blocks, all of which are cutouts of the NaCl type. For SnSe contents between x = 5 and x = 0.5, several new phases were discovered. Next to, for example, Sn4Bi2Se7 (x = 4) in the NaCl structure type and SnBi4Se7 (x = 0.5) in the layered defect GeSb2Te4 structure type, there are at least four compounds (0.8 <= x <= 3) with lillianite-like structures built up from distorted NaCl-type slabs (L4,4-type Sn2.22Bi2.52Se6, L4,5-type Sn9.52Bi10.96Se26, L4,7-type Sn11.49Bi12.39Se30, and L7,7-type Sn36Bi3.6Se9). For two of them (L4,7 and L7,7), the cation distributions were determined by resonant X-ray scattering, which also confirmed the presence of significant amounts of cation vacancies. Thermoelectric figures of merit ZT range from 0.04 for Sn4Bi2Se7 to 0.2 for layered SnBi4Se7; this is similar to that of the related compounds SnBi2Te4 or PbBi2Te4. Compounds of the lillianite series exhibit rather low thermal conductivities (similar to 0.75 W/mK for maximal ZT). More than other "sulfosalts", compounds in the pseudobinary system SnSe-Bi2Se3 adapt to changes in the cation-anion ratio by copying structure types of compounds containing lighter or heavier homologues of Sn, Bi, or Se and can incorporate significant amounts of vacancies. Thus, (SnSe)(x)Bi2Se3 is a multipurpose model system with vast possibilities for substitutional and structural modification aiming at the optimization of thermoelectric or other properties.