Alkali metal thallides have been known since the report of E. Zintl on NaTl in 1932. Subsequently, binary and ternary thallides of alkali metals have been characterized. At an alkali metal proportion of approximately 33% (A:Tl~1:2, A = alkali metal), three different unique type structures are reported: K49Tl108, Rb17Tl41 and A(15)Tl(27) (A = Rb, Cs). Whereas Rb17Tl41 and K49Tl108 feature a three-dimensional sublattice of Tl atoms, the A(15)Tl(27) structure type includes isolated Tl-11 clusters as well as two-dimensional Tl-layers. This unique arrangement is only known so far when the heavier alkali metals Rb and Cs are included. In our contribution, we present single-crystal X-ray structure analyses of new ternary and quaternary compounds of the A(15)Tl(27) type structure, which include different amounts of potassium. The crystal structures allow for the discussion of the favored alkali metal for each of the four Wyckoff positions and clearly demonstrate alkali metal dependent site preferences. Thereby, the compound Cs2.27K12.73Tl27 unambiguously proves the possibility of a potassium-rich A(15)Tl(27) phase, even though a small amount of cesium appears to be needed for the stabilization of the latter structure type. Furthermore, we also present two compounds that show an embedding of Tl instead of alkali metal into the two-dimensional substructure, being equivalent to the formal oxidation of the latter. Cs14.53Tl28.4 represents the binary compound with the so far largest proportion of incorporated Tl in the structure type A(15)Tl(27).