A feasibility analysis of a hybrid fusion–fission system consisting of a two-stage spherical subcritical cascade driven by a Plasma Focus device is presented. The analysis is based on the one-group neutron diffusion equation, which was appropriately cast to assess the neutronic amplification of a spherical configuration. A design chart was produced to estimate the optimum dimensions of the fissile shells required to achieve different levels of neutron amplification. It is found that cascades driven by Plasma Focus of tens of kJ are feasible. The results were corroborated by means of Monte Carlo calculations.