  We analyze the possibility that several instability points may be formed, due
to the Paczy\'nski mechanism of violation of mechanical equilibrium, in the
orbiting matter around a supermassive Kerr black hole. We consider recently
proposed model of ringed accretion disk, made up by several tori (rings) which
can be corotating or counterrotating relative to the Kerr attractor due to the
history of the accretion process. Each torus is governed by the general
relativistic hydrodynamic Boyer condition of equilibrium configurations of
rotating perfect fluids. We prove that the number of the instability points is
generally limited and depends on the dimensionless spin of the rotating
attractor.
