The evolution of sintering stress, bulk viscosity, and densification rate during the intermediate stage and the final stage of sintering of random aggregates of particles is simulated using a new model able to account for the monotonous increase in the coordination number during sintering. For the intermediate stage, the representative volume element is a cone of revolution whereas, for the final stage, it is volume centered on a closed pore located at quadruple point. Care is taken to warrant the continuity between the two models at the transition between the two stages. Computations allow tracing the variation in sintering stress and bulk viscosity with relative density, coordination, and dihedral angle during the two stages, as well as at the transition between them. They show how, as a result, densification rate is enhanced by the increase in coordination. The model is assessed via comparison of the computed curves with the predictions of previous models based on periodic 3D arrangements, in which grain coordination number is constrained to jump between integer values. The agreement is generally very good in spite of the different approximations involved.