The exact nature of the induced coupled-fields of anisotropic magneto-electro-elastic ellipsoidal inclusions, multi-inclusions, and inhomogeneities with non-uniform eigenfields under polynomial magneto-electro-elastic far-field loadings is of particular interest. For the sake of prediction of the induced coupled-fields of magneto-electro-elastic multi-inclusions due to piecewise polynomial generalized eigenfields several theorems and corollaries are stated and proved. Some classes of impotent generalized eigenfields associated with encapsulated ellipsoidal multi-inclusion result in vanishing generalized disturbance strains within the innermost ellipsoidal domain. On the other hand, it is found that there are certain classes of impotent generalized eigenfields for which the generalized disturbance stresses vanish everywhere. Furthermore, it is proved that there exists a unique equivalent magneto-electro-elastic inclusion associated with an anisotropic magneto-electro-elastic ellipsoidal inhomogeneity subjected to polynomial far-field loadings. It is shown that associated with every anisotropic magneto-electro-elastic ellipsoidal inhomogeneity, there exists a set of infinite numbers of far-field loadings for which the inhomogeneity does not induce any disturbance generalized stresses anywhere within the entire medium. In other words, under certain far-field loadings the inhomogeneity is not sensed by the surrounding magneto-electro-elastic medium.