  A generalization of the Polyakov-Koba-Nielsen-Olesen scaling law of the
multiplicity distributions P(n,s) is developed. It states that a suitable
change in the normalization point of P(n,s) compensated by a rescaling can
restore data collapsing onto a universal curve if the original scaling rule is
violated. We show that the iteratively executed transformation of P(n,s) can be
viewed as varying the collision energy. The e+e- and p-pbar multiplicity data
at top energies are found to exhibit a fixed point property of the iteration.
