The original ideas which lead to the development of MMP-3D are still very much in use. However during the past years, there has been some recent improvements which lead to both the hybridization and generalization of the method. In particular, there has been a generalization for the sources or basis functions, to allow the computation of special geometries. Also, a combination with line theory has lead to a new type of boundary equations to allow the computation of fields going through shieldings. The general theoretical aspects will be the main purpose of this paper.