Multiphoton ionization of helium is investigated in the superintense field regime, with particular emphasis on the role of the electron-electron interaction in the ionization and stabilization dynamics. To accomplish this, we solve ab initio the time-dependent Schrodinger equation with the full electron-electron interaction included. By comparing the ionization yields obtained from the full calculations with corresponding results of an independent-electron model, we come to the somewhat counterintuitive conclusion that the single-particle picture breaks down at superstrong field strengths. We explain this finding from the perspective of the so-called Kramers-Henneberger frame, the reference frame of a free (classical) electron moving in the field. The breakdown is tied to the fact that shake-up and shake-off processes cannot be properly accounted for in commonly used independent-electron models. In addition, we see evidence of a change from the multiphoton to the shake-off ionization regime in the energy distributions of the electrons. From the angular distribution it is apparent that correlation is an important factor even in this regime.