The formulae of single-atom and two-atom vdW potential of ground-state electric atoms in the presence of arbitrary arrangements of linear magneto-electric bodies have been generalized to atoms with both electric and magnetic polarizabilities within the framework of macroscopic quantum electrodynamics. To this end, we have extended an existing quantization scheme for a system consisting of a medium-assisted electromagnetic field and an atom with spinless constituents to a many-atom case, where in order to account for the paramagnetic atom-field interactions correctly, the spin of the constituents of the atoms are involved. The quantization is followed by introducing a Hamiltonian whose consistency is examined by showing that it leads to the dynamical Maxwell equations and Newton equation of motion as the equations of motion for the electromagnetic field and for the charged particles, respectively. For the cases where the atoms under consideration are embedded in host media, the local-field corrections to the vdW potentials are presented using the real-cavity model. The corrections come into effect via frequency-dependent factors, which depend on the magneto-electric properties of the media at the location of the atoms. In all the examples throughout this work the consistency of the obtained expressions for the potentials with the electromagnetic duality principle is verified. In particular, in the cases where the atoms are embedded in host magneto-electric media, the local-field corrections are required to this end. To illustrate the effect of the bodies on the vdW interaction potential some numerical results are presented. Finally, the body-induced enhancement or reduction of the vdW interatomic potential (shown by the numerical results) in the nonretarded limit are interpreted, qualitatively, exploiting the method of image-charges.