In nonlinear nanophotonics, scalable sequential signal transformation of second-harmonic generation (SHG) in pure plasmonic waveguides remains challenging. Precise phase matching becomes instrumental to achieve efficient SHG and enable sequential generation of nonlinear signals. We experimentally demonstrate the phase matching in SHG between two orthogonal modes through dispersion engineering. Accurate tuning of plasmonic two-wire transmission-line (TWTL) design parameters results in SHG from the antisymmetric excitation mode being approximately 15 times stronger than that from the symmetric excitation mode, greatly raising the conversion efficiency to 0 . 021% . Simultaneously, the measured devices show that the phase matching extends our TWTL operational length at least up to 18 𝜇𝑚 . Based on the improved efficiency and operational length, we demonstrate a multi-stage device capable of performing polarization-dependent switching between the linear propagation of SHG and frequency up-conversion in the later stages. We further realize a nonlinear OR logic operation using a single 18 𝜇𝑚 long waveguide. These results underscore the potential of phase-matched plasmonic TWTLs for compact, efficient, and scalable nonlinear optical circuitry.