The rules for layering electron orbitspheres in a multi-electron atom are complex, but generally follow the pattern set down for spherical harmonics and minimization of energy. That is, more than one electron may occupy the same orbital radius, but they must occupy distinct spherical harmonics. Unsurprisingly, the pattern follows the familiar s, p, d, f orbitals we all learned from Chemistry. For each of the of ions with a given number of electrons, n, you can determine an ionization energy for a central charge +Z (where Z >= n) from electrical and magnetic interactions between the different electrons. The combination of orbitals that minimizes the ionization energy will depends only on n, and the calculation can then be easily calculated for all Z corresponding to that n.
This leads to a straight forward determination of all ionization energies for all ions of n electrons and Z protons. In fact, this can be done in a spreadsheet, which I have successfully replicated on my own for all ions of 1 through 20 electrons.
To be honest, this is the only reason I ever became interest in Mills' theory, and remain interested to the present. Back in the day, my Nobel winning Chem prof. assured my Freshman class that such a calculation was impossible. He waxed on about three-body problems and the like. Yet, following Mills' theory, I can perform this calculation quite easily in Excel. I'd like to get to the bottom of this mystery.