Lewis acid doping of organic semiconductors (OSCs) opens up new ways of p-type doping and has recently become of significant interest. As for the mechanistic understanding, it was recently proposed that upon protonation of the OSC backbone, electron transfer occurs between the protonated polymer chain and a neutral chain nearby, inducing a positive charge carrier in the latter [Nat. Mater. 18, 1327 (2019)]. To further clarify the underlying microscopic processes on a molecular level, in the present work, we analyze the influence of protons on the electronic properties of the widely used PCPDT–BT copolymer. We find that single protonation of the polymer chain leads to the formation of a polaron coupled to the position of the proton. Upon protonation of the same chain with a second proton, an intrachain electron transfer occurs, leaving behind a polaron largely decoupled from the proton positions. We also observe the possibility of an interchain electron transfer from a neutral chain to a double protonated chain in agreement with the mechanism recently proposed in the literature. The simulated vertical excitation spectra for an ensemble of protonated species with different amounts of protons enable a detailed interpretation of experimental observation on PCPDT–BT doped with the Lewis acid BCF. Our results further suggest that multi-protonation plays an important role for completing the mechanistic picture of Lewis acid doping of OSCs.