In earlier work, reported at previous INMM conferences, we extended the methodology of multiplicity counting in nuclear safeguards beyond the point model. This was achieved by elaborating the one-speed stochastic transport theory of the calculation of the so-called multiplicity moments, i.e. the factorial moments of the number of neutrons emitted from a fissile item, following a source event from an internal neutron source (spontaneous fission and (alpha,n) reactions). Calculations were made for spheres and cylinders of various shapes. In all our work so far, the material of the items was homogeneous, and the distribution of the internal source was assumed to be uniformly distributed within the item, with the neutron emission assumed to be isotropic. In the present work the calculations are extended to the case of a point source in the centre of either a solid sphere or of a spherical shell. Further, the effect of including isotropic elastic scattering, in addition to fission (which is not possible in the point model) is also investigated. This work describes the extension of the theory and provides thorough quantitative results, quantifying the effect of a localised source instead of homogeneously distributed ones, the effect of the central cavity, and the effect of elastic scattering. The calculations were inspired by recent measurements made by the DNNG group of the NERS Department of the University of Michigan on the Rocky Flats shells.