Is the Kerr black hole a super accelerator?

A number of long-standing puzzles, such as the origin of ultrahigh-energy cosmic rays, could perhaps be solved if we found a mechanism for effectively transferring energy from black holes to particles and, correspondingly, accelerating the latter to (unboundedly, as long as we neglect the back reaction) large velocities. As of today the only such candidate mechanism in the case of the non-extreme Kerr black hole is colliding a particle that freely falls from infinity with a particle whose trajectory is subject to some special requirements to fulfil which it has to be suitably corrected by auxiliary collisions. In the present paper we prove that---at least when the relevant particles move in the equatorial plane and experience a single correcting collision---this mechanism does not work too. The energy of the final collision becomes unboundedly high only when the energies of the incoming particles do.