An investigation was made of the processes of collective acceleration of protons in vacuum in a system with an insulated anode and trans-anode electrodes, which were insulated or grounded, in high-current Tonus and Vera electron accelerators. The influence of external conditions and parameters of the electron beam on the efficiency of acceleration processes was investigated. Experiments were carried out in which protons were accelerated in a system with trans-anode electrodes. A study was made of the influence of a charge prepulse and of the number of trans-anode electrodes on the energy of the accelerated electrons. A system with a single anode produced Np=1014 protons of 2Ee < Ep < 3Ee energy. Suppression of a charge prepulse increased the proton energy to (6 8)Ee and the yield was then 1013. The maximum proton energy of 14Ee was obtained in a system with three trans-anode electrodes. A possible mechanism of proton acceleration was analyzed. The results obtained were compared with those of other investigations. Ways of increasing the efficiency of this acceleration method were considered.