Two-proton (2p) radioactivity provides fundamental knowledge on the three-body decay mechanism and the residual nuclear interaction. In this work, we propose decay width formulae in the extended R-matrix framework for different decay mechanisms, including sequential 2p decay, diproton decay, tri-body decay, and sequential two-diproton decay. The diproton and tri-body formulae, combined with information on the two-nucleon transfer amplitude and Wigner single-particle reduced width, can reproduce well experimental 2p radioactivity half-lives. For the case of 67Kr, theoretical predictions for direct 2p decay give much larger half-lives than the recent measurement from RIKEN. A combination of direct and sequential 2p emission is analyzed by considering a small negative one-proton separation energy and a possible enhanced contribution from the p-wave component. The present method predicts that 71Sr and 74Zr may be the most promising candidates for future study on 2p radioactivity. Our model gives an upper limit of 55(4) keV for the decay width of 4p emission in recently found four-proton resonant nuclide, 18Mg, which agrees with the observed width of 115(100) keV.