Subsequent scaling steps in the solution for the potential are mainly intended to provide a finer mesh on which to evaluate the potential, i.e. without any significant global change in the potential compared to the first scaling step step.
Situations can arise when it is difficult to achieve near convergence of the solution on the first scaling step. For example, a small protrusion on the end of the tip forces the use of a fine grid, and hence many grid points may be needed to achieve a large enough simulation region. (Actually, tip protrusions have not been generally used in SEMITIP simulations, so they may lead to a variety of problems other than just limited convergence). Separately, in situations of self-consistency, the self-consistency loop is applied only in the final scaling step of the computation, so if significant changes in the solution are produced by the self-consistency, then care must to taken to use sufficiently tight convergence parameters for this loop.