The maximum stable pedestal pressure has been shown to increase with core pressure and, in combination with core transport effects, this can lead to a positive feedback mechanism. However, the effect is shown to saturate for a high β in ASDEX-Upgrade simulations [Wolfrum et al. "Impact of wall materials and seeding gases on the pedestal and on core plasma performance,"Nucl. Mater. Energy 12, 18 (2017)]. In this paper, it is numerically investigated whether this effect appears in ITER plasmas, using ideal MHD numerical codes HELENA and MISHKA for different ITER scenarios, in a range of plasma conditions: two inductive scenarios at 7.5 MA/2.65 T and 15 MA/5.3 T and one steady-state scenario at 10 MA/5.3 T. For all scenarios, reference cases for ITER plasmas were taken as a starting point. No pedestal pressure saturation is found for the inductive scenarios, gradually growing up to the global βN limit, which is determined by the Troyon limit. On the contrary, for the 10 MA/5.3 T steady-state scenario, the maximum stable pedestal pressure does not depend on the total β and it is limited by low-n kink-peeling modes, as opposed to high-n peeling-ballooning modes that limit the maximum attainable pedestal height in the inductive scenarios. This core-edge MHD stability feedback loop has been investigated for two assumptions regarding the scaling of the pedestal width with β p, ped ¯, using either a constant pedestal width or when scaling it as Δ ψ N β p, ped ¯ 1 / 2. A stronger core-edge MHD stability feedback is observed for the varying pedestal width for the inductive plasma scenarios, which is closer to the experimental results from JET [Challis et al. "Improved confinement in JET high plasmas with an ITER-like wall,"Nucl. Fusion 55(5), 053031 (2015)], but not for the steady-state one. Finally, the pressure achieved according to this core-edge feedback stability analysis is compared to the plasma pressure achievable on the basis of the energy confinement IPB98(y,2) scaling for various assumptions regarding the scaling of core plasma confinement with heating power.