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 DP_N 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.