A kinematically complete experiment for simultaneous ionization of a projectile and target has been performed for 3.6 MeV/u C2+ on He collisions measuring the final vector momenta of the He1+ recoil ion and of two electrons (projectile, target) in coincidence with the emerging C3+ projectile. The feasibility of an event-by-event separation of the various reaction channels, among them the ionization of C2+ by the interaction with a quasifree target electron, is demonstrated in agreement with six-body classical trajectory Monte Carlo calculations, paving the way to kinematically complete electron-ion scattering experiments.