Goos–Hänchen (GH) shift, a distinctive optical phenomenon, has attracted considerable interest due to its extensive potential applications in high-sensitivity sensing, optical switching, and nanoscale photonic devices. In this work, a multilayer heterostructure composed of alternating layers of black phosphorene (BP) and silicon (Si) is designed, and its GH shifts are systematically investigated with the aim of achieving large-amplitude, electrically tunable GH shifts in the near-infrared region. Furthermore, we elaborate on the underlying phase-modulation mechanisms and the sensing performance of the proposed structure. Using the transfer matrix method and the optical conductivity of BP calculated via the Kubo formalism, we comprehensively examine the cooperative effects of polarized modes, structural periodicity, incident optical energy, and external voltage on the evolution of the reflection phase and the consequent GH displacement. The results indicate that the incorporation of BP, through the introduction of complex surface conductivity, significantly modifies the phase response of transverse magnetic (TM) waves near the traditional Brewster angle, transforming the original \textπ -phase jump into a continuous and differentiable phase transition. This effect enables a GH shift as large as 40 \lambda even in a single-period structure. Although transverse electric (TE) waves do not exhibit Brewster-angle behavior, several-wavelength-scale GH shifts can still be achieved under near-grazing incidence due to Fabry–Pérot interference. Further analysis reveals that increasing the number of (BP–Si) periods steepens the slope of the reflection phase, thereby enhancing the GH shift of the TM wave from 40 \lambda to 128 \lambda in a four-period structure at an incident optical energy of 1.52 eV. In addition, the application of an external voltage modulates the energy bandgap and optical conductivity of BP, providing dual control over both the magnitude and angular position of the GH shift. For example, under an external voltage of 0.5 eV, the maximum GH shift of the TM wave in a single-period structure increases from 184 \lambda to 586 \lambda when incident optical energy is 1.4 eV. The structure also exhibits an ultrahigh refractive index sensitivity exceeding 10⁵ \lambda /\mathrmRIU toward variations in the refractive index of the terminal medium, with further enhancement under electrical bias. These findings reveal the mechanism through which two-dimensional materials induce phase continuity and enhanced GH shifts, while demonstrating the strong potential of BP-Si multilayers for the development of tunable near-infrared photonic components and high-sensitivity optical sensing platforms.