Herein, a sub-40 nm fractional hollow AuAg nanobox is asymmetrically filled with Ag atoms inside the nanobox until it is gradually transformed into a solid AuAg nanobox, and the discrete dipole approximation (DDA) method is applied to calculate the corresponding extinction spectra in this process. It is observed that the height of the inner Ag core could cause a non-monotonous shift of the surface plasmon resonance (SPR) band, which first has a linear blue shift and then a near-exponential red shift, indicating that the height of the inner Ag core could be presented as a key factor to tune the core-dependent non-monotonous SPR shift. A local electric field analysis reveals that the non-monotonous SPR shift may be attributed to the switching of plasmon coupling, then inducing the SPR properties of nanoshell and dimer, respectively. Furthermore, we find that the refractive index of both the dielectric cavity and ambient medium could tune the switching threshold of the Ag core height corresponding to the plasmon coupling. It is also revealed that the switching of plasmon coupling could significantly affect the local electric field intensity and its distribution. Consequently, we believe that the asymmetrical Ag core could increase the tunability of an SPR shift and change the local electric field distribution, which provides the potential for SPR-based biosensing and surface-enhanced Raman scattering (SERS) applications.