A multilayer structure using graphene on a silicon waveguide is introduced and optimized to operate as a tunable TE-pass polarizer at 1310 nm or 1550 nm, a tunable TE/TM modulator at 1310 nm or 1550 nm, and a dual operation as a modulator at 1310 nm and a polarizer at 1550 nm. The analysis is based on the waveguide structure modal loss, the 2D graphene layer optical properties and its dependency on the applied chemical potential. The optimization is done by varying waveguide height and choosing the one with best figures of merit for each individual case and for the dual operation, the value that causes the least impairment overall is chosen. The polarizer tunability at 1310 nm or 1550 nm is attainable setting the applied chemical potential range from 0.55–0.65 eV or 0.45–0.55 eV, respectively. For the modulator tunability at 1310 nm or 1550 nm, the applied chemical potential range from 0.45–0.55 eV or 0.35–0.45 eV, respectively. The optimized waveguide silicon layer around 210 nm guarantees an extinction ratio better than 0.056 dB/µm for the polarizer and better than 0.045/0.133 dB/µm for the TE/TM modulator at 1310 nm, and better than 0.034 dB/µm for polarizer and better than 0.053/0.137 dB/µm for TE/TM modulator at 1550 nm. Further, the setting the chemical potential range at 0.45–0.55 eV, allows dual polarizer-modulator operation, with the modulator operating at 1310 nm and the polarizer operating at 1550 nm, presenting an extinction ratio better than 0.045 dB/µm and 0.034 dB/µm respectively. In all situations analyzed, insertion loss is lower than 0.007 dB/µm. The advantage of the structure in comparison with other similar devices relies in its versatility to operate as both modulator and polarizer, in different wavelengths, via a proper choosing of the applied chemical potential.