As a complement to some new breakthroughs on global almost disturbance decoupling problem with stability for nonlinear systems, in a recent note, we identified a class of unstable zero dynamics that are allowed to be affected by disturbances. The class of the unstable zero dynamics identified in that note is linear and have all the poles at the origin. In this paper, we enlarge such a class of zero dynamics to include any linear system with all its poles in the closed left-half plane. The condition on the way the disturbance affects this part of zero dynamics is also identified. This enlargement is due to a new scaling technique that views each pair of jw axis zeros as a "generalized integrator" and transforms the zero dynamics into a number of chains of "generalized integrators".