An interesting idea that we are in the process of exploring, and it is, thus, not developed here, is that of a "nested exact factorization". In this case, we would consider the marginal photon-nuclear amplitude χ(q, R,t) and the corresponding TDSE as the starting point of a new EF, which would lead to introduce, for instance, a marginal nuclear amplitude and a conditional photonic amplitude. The new evolution equations derived in this way, still under the effect of the TDPES and the TDVP, could potentially lead to develop more appropriate approximations for the photon dynamics. While, as mentioned above, this avenue is still to be fully investigated, the simplest approximation to such a photon-nuclear EF is an uncorrelated Hartree product of the marginal photonic η(q,t) and of the marginal nuclear ζ (R,t) wavefunction, namely