As previously done for the treatment of molecular processes beyond the BOA, we discuss here the exact factorization (EF) to go beyond the cavity-BOA. In the original formulation, the electron?nuclear wavefunction is factored as a marginal nuclear wavefunction and a conditional electronic wavefunction -conditional on the nuclear positions. However, since no approximation is made on the typical time scales of the dynamics of the two subsystems, the EF has been extended to factor different "kinds" of multicomponent many-body wavefunctions. In this work, we focus on the PEN wavefunction. Note that the choice of marginal and conditional wavefunctions is quite arbitrary but always applicable when the partial normalization condition (PNC) is imposed on the conditional term (see discussion below). Specifically, as briefly described in the Introduction, various authors have already introduced the EF formalism to analyze light-matter problems, namely electron-photon and PEN systems. Maitra and coworkers proposed Ψ(r, q, R,t) = χ N (R,t)Φ N (r, q,t; R) = χ P (q,t)Φ P (r, R,t; q) = χ E (r,t)Φ E (R, q,t; r), where the marginal amplitudes are the nuclear (N), the photonic (P) or the electronic (E) wavefunctions, respectively, and looked in some details into the first and second ideas . Here, we explore an alternative possibility, where the PEN wavefunction is factored as a single product of a marginal photon-nuclear wavefunction, χ(q, R,t), and a conditional electronic wavefunction parametrically dependent on the photon-nuclear coordinates, Φ(r,t; q, R), i.e., Ψ(r, q, R,t) = χ(q, R,t)Φ(r,t; q, R)