Surface plasmon resonance (SPR) sensing on a silicon-based platform is considered. We have studied properties of SPR in a combined silicon-dielectric layer-gold film-sample medium structure and established conditions of the simultaneous excitation of two plasmon polariton modes that provide narrow and well-separated minima of the reflected intensity. It has been shown that the external mode over the gold-sample medium interface demonstrates a highly sensitive response to a change in the refractive index of the sample medium, whereas the internal mode over the dielectric-gold interface is almost insensitive to medium parameters. We propose that the internal mode can be used as an effective reference zero point for miniature and portable SPR-based systems designed for field and multichannel sensing.