We propose numerically an approach to narrow the plasmon linewidth and enhance the magnetic near field intensity at a magnetic hot spot in a hybridized metal-insulatormetal (MIM) structure. First we insert in part of the dielectric layer of the MIM, at its center, another dielectric material of a high refractive index (HRI). This results in an increase in the magnetic near field enhancement of the magnetic plasmon (MP) resonance by 82% compared with the MIM without the HRI material. We then couple this enhanced MP resonance to a propagating surface plasmon polariton (SPP) to achieve a further enhancement of 438%. The strong coupling between the MP and the SPP is demonstrated by the large anti-crossing in the reflection spectra. The resulting maximum magnetic field enhancement at the gap is ~ |H / Hi|² = 3555.