In this research, we consider plasmon tunneling through the intrinsic chemical potential barriers using the Schrödinger-Poisson model. The Schrödinger-Poisson system is reduced to the linear coupled pseudoforce system, and the electrostatic as well as wavefunction solutions are derived and used to obtain the transmittivity and reflectivity of plasmon excitations through the double and triple metallic barriers with various parameter settings. It is remarked that the choice of chemical potential (Fermi energy for metals) in quantum barriers has a significant effect on the transmission amplitude of collective electron excitations. For triple metallic barriers, it is found that the transmittivity spectrum possesses distinct transmission valleys in the energy spectrum, which may be attributed to the interactions of single-electron oscillations with the collective electrostatic excitations. Current research can have important applications in fast quantum tunneling devices with intrinsic chemical potential barriers and helps in the development of rapidly growing fields of plasmonics and nanometallic technology.