The spin–orbit interaction of light is universal in the process of light scattering, and an important aspect is the spin Hall effect. The spin Hall effect of light also exists in a three-dimensional (3D) system. When circularly polarized light is incident on a spherical particle, the transverse displacement of the particle relative to the scattering plane can be observed due to the spiraling of the Poynting vector in the far field. In general, the spin Hall shift of light is negligible and difficult to detect in experiments. In this paper, we use a high-refractive-index (HRI) core-shell structure to excite high-order multipoles and explore the interaction between different order multipoles to enhance the spin Hall shift in the microwave band. We show that there exist some angles that increase the spin Hall shift when two particular multipoles are equal and dominated. Our work provides a new perspective for understanding the interaction between light and particles and enhances the spin Hall shift of the sphere in the microwave band.