By means of angle-resolved photoemission spectroscopy measurements, the electronic band structure of the three-dimensional PbBi₄Te₇ and PbBi₆Te₁₀ topological insulators is compared. The measurements clearly reveal coexisting topological and multiple Rashba-like split states close to the Fermi level for both systems. The observed topological states derive from different surface terminations, as confirmed by scanning tunneling microscopy measurements, and are well-described by the density functional theory simulations. Both the topological and the Rashba-like states reveal a prevalent two-dimensional character barely affected by air exposure. X-ray and valence band photoemission measurements suggest Rashba-like states stem from the van der Waals gap expansion, consistently with density functional theory calculations.