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Structural engineering of topological bulk materials is systematically explored with regard to the incorporation of the buckled bismuth layer [Bi₂], which is a 2D topological insulator per se, into the layered BiTeI host structure. The previously known bismuth telluride iodides, BiTeI and Bi₂TeI, offer physical properties relevant for spintronics. Herewith a new cousin, Bi₃TeI (sp.gr. R3m, a = 440.12(2) pm, c = 3223.1(2) pm), joins the ranks and expands this structural family. Bi₃TeI = [Bi₂][BiTeI] represents a stack with strictly alternating building blocks. Conditions for reproducible synthesis and crystal-growth of Bi₂TeI and Bi₃TeI are ascertained, thus yielding platelet-like crystals on the millimeter size scale and enabling direct measurements. The crystal structures of Bi₂TeI and Bi₃TeI are examined by X-ray diffraction and electron microscopy. DFT calculations predict metallic properties of Bi₃TeI and an unconventional surface state residing on various surface terminations. This state emerges as a result of complex hybridization of atomic states due to their strong intermixing. Our study does not support the existence of new stacking variants BiₓTeI with x > 3; instead, it indicates a possible homogeneity range of Bi₃TeI. The series BiTeI–Bi₂TeI–Bi₃TeI illustrates the influence of structural modifications on topological properties.