Important would be to see how to build the many electron wave function (symmetry) from the ("empty") orbitals.
And thats how I said simply by product formation.
And now you do the D4h Eg JT example for 1 and then for 2 electrons
then one should see that for each 2nd order example there should be a 1 to 1 map to a 1st order case
that should be non trivial and is in some way very important for us. since the good real world expamples are 2-e cases ...
and our ideas where derived for the one-electron world
Accodring to my JT specialist that is something also others have observed but nothing is worked out (and there is also the sad thing the in the end you can step down in all cases until C1 and A ....; but that must not worry us since it applies for the whole field so to say, and thats not dead, far from it actually)