By means of angle-resolved photoemission spectroscopy (ARPES) measurements, we unveil the electronic band structure of three-dimensional PbBi₆Te₁₀ topological insulator. ARPES investigations evidence multiple coexisting Dirac surface states at the zone-center of the reciprocal space, displaying distinct electronic band dispersion, different constant energy contours, and Dirac point energies. We also provide evidence of Rashba-like split states close to the Fermi level, and deeper M- and V-shaped bands coexisting with the topological surface states. The experimental findings are in agreement with scanning tunneling microscopy measurements revealing different surface terminations according to the crystal structure of PbBi₆Te₁₀. Our experimental results are supported by density functional theory calculations predicting multiple topological surface states according to different surface cleavage planes.