Given the small level of residual transport within the edge pedestal of H-mode tokamak plasmas, even low levels of additional transport within this region (e.g. due to ripple losses of thermal ions or edge ergodization) can have a significant effect on pedestal performance. Such additional transport will affect the shape of the plasma profiles within the pedestal. In this paper, the dependence of the sustainable level of pedestal pressure gradient and toroidal edge current density on the pedestal plasma profile shapes is systematically studied by means of ideal linear magnetohydrodynamic stability analysis. It is concluded that the further inside the separatrix the maximum pressure gradient is reached, the larger the level of pressure gradient that the plasma can sustain is. It is also found that the further inside the separatrix the pressure gradient maximum is located, the wider the eigenfunctions of the unstable modes are and the smaller the toroidal mode number of the most unstable mode is.