A new linearization method for optical transmitters based on directly modulated lasers (DMLs), named the Stretched A method, was proposed in Parts I and II of this work. Parts I and II presented the theoretical framework of the method for non-return-To-zero (NRZ) modulation and related detailed simulation and experimental results. Here, we extend the method to pulse amplitude modulation schemes (PAM). Focussing on 4-level PAM (PAM-4), we present the theoretical background and discuss implementation options. A simplified variation of the method for the generation of PAM signals with a significantly lower number of sub-currents is proposed. Simulation studies for PAM-4 transmission at 50 GBaud (100 Gb/s) and an experimental proof-of-principle demonstration at 16 GBaud (32 Gb/s) are reported based on 850 nm vertical-cavity surface-emitting lasers (VCSELs). For PAM-4, products of effective eye diagram areas ({\boldsymbol{PS}}) of 0.6 × 10-5 and 43 × 10-5 before and after applying the Stretched A method were measured, demonstrating an improvement ratio of ∼72. The sensitivity and tolerances of the method are analyzed using simulation and experiment.