The linac and the 3 GeV rapid-cycling synchrotron (RCS) at the Japan Proton Accelerator Research Complex (J-PARC) were designed to provide 1-MW proton beams to the following facilities. Due to the improvement of the accelerator system, we accelerated a 1-MW beam with a small beam loss. The lack of anode current in the radiofrequency (RF) cavity, rather than beam loss, limits the RCS beam power. Recently, we developed a new acceleration cavity that can accelerate a beam with a low anode current. This new cavity enables us to reduce the requirement for the anode power supply and accelerate a beam of more than 1 MW. We considered how to achieve beam acceleration beyond 1 MW. So far, a beam of up to 1.5 MW is expected to be accelerated after replacing the RF cavity. We also studied to achieve an up to 2-MW beam in J-PARC RCS.