In this paper we describe some recent developments in the Method of Characteristics (MOC) for three-dimensional (3D) extruded geometries in the nuclear reactor analysis code APOLLO3®. We discuss the parallel strategies implemented for the transport sweep of the MOC solver in the OpenMP framework, and introduce the 3D version of the DPN operator that is customarily used in APOLLO2 to accelerate MOC convergence. In order to provide good physical results, we have also coupled the MOC with the self-shielding environment of APOLLO3®. We describe, in particular, the coupling techniques necessary to implement a full subgroup cross-section self-shielding method and a specialized version of the Tone self-shielding technique. In this framework, we use part of the tracking method used for the 3D calculation to provide the two-dimensional Collision Probability Method (CPM) coefficients necessary to produce the self-shielding calculations. We will show some important computational speedups also in the CPM of APOLLO3® with respect to the APOLLO2 CPM equivalent implementation, including the parallelization issue. Finally, we will compare our approach toward a Monte Carlo calculation of a fast breeder reactor hexagonal assembly representing a fertile-fissile interface.