We investigate the evolution of both the occupied and unoccupied electronic structure in representative compounds of the infinitely adaptive superlattice series (Sb2)m−Sb2Te3 (m=0–3) by means of angle-resolved photoemission spectroscopy and time-delayed two-photon photoemission, combined with first-principles band-structure calculations. We discover that the topological nature of the surface states and their spin texture are robust, with dispersions evolving from linear (Dirac-like) to parabolic (Rashba-like) along the series, as the materials evolve from semiconductors to semimetals. Our findings provide a promising strategy for engineering the topological states with the desired flexibility needed for realizing different quantum phenomena and spintronics applications.