The toroidal magnetohydrodynamic (MHD) code MARS-F (Liu et al 2000 Phys. Plasmas7 3681) is applied to numerically investigate multiple MHD instabilities in high-βN (βN is the beta normalized) toroidal plasmas with reversed magnetic shear, and with different radial separations between the two q = 2 rational surfaces. A resistive wall is also taken into account. In the small regime, it is found that a finite βN leads to multiple branches of the double tearing mode (DTM). The beta normalized has a stabilizing effect on the most unstable branch. There exists a critical value βNc, above which the real frequency of the most unstable mode becomes finite due to the favorable average curvature effect (Glasser et al 1975 Phys. Fluids18 875). Moreover, the critical value βNc decreases with increasing plasma resistivity In the large regime, on the other hand, finite beta normalized can help to transform the two DTM branches into an external kink mode (EKM). Increasing βN can also couple two single tearing modes, forming a DTM. In the intermediate regime, interestingly, a new branch with EKM structure appears, which successively couples with the other two branches as increases, recovering the EKM found in the large limit. Characteristics of the eigenmode structures in different regimes are compared and analyzed in detail. Furthermore, the properties of the high-βN MHD instabilities, with higher toroidal mode number n, are also investigated. It is found that, in the small limit, the growth rate always first increases and then decreases with n, forming a broad n spectrum. The critical value decreases with n. In the large limit, however, the growth rate of the n = 2 mode is strongly reduced with increasing βN.