One of the aims of new circular collider projects is further increase in their luminosity. A high electromagnetic field of space charge at the meeting points limits the achievable current densities and consequently the luminosity. Nonlinear focusing compensation in a storage ring done by the opposite-charge beam circulating in another storage ring was proposed and tested many years ago. Ya. S. Derbenev has shown that such a scheme suffers from tune shifts of coherent betatron oscillations, which move betatron frequencies toward the nearest integer or half-integer resonance. In this paper, the collider based on electron energy recovery linac (ERL) and "figure-8" positron storage ring with beams of equal currents is considered. Positrons are circulating in a two-loop storage ring (positron-positron collider), and electron-electron collider uses ERL, as in original Tigner's proposal. Thus, a collision of four bunches and space-charge compensation in a multi-bunch mode can be ensured. The mathematical and numerical analysis of this configuration is presented.