Best-fit SED models and residuals (with respect to the PRISM spectrum) for four model variations, constructed as different mixtures of (dust-reddened) stellar population and power-law AGN model components. These AGN models do not consider the possible reddening by absorbing dense gas, which we explore in Section 6.4. The right panels show zoomed-in images of the region around the Balmer break. From top to bottom: the fiducial galaxy-only model from Prospector; a galaxy + AGN model that maximises the stellar contribution, fit with Prospector (the maximal M_* model of Wang et al. 2024a); the galaxy + AGN model following Labbe et al. (2024), but fitting only hydrogen emission lines instead of a forest of metal lines; the galaxy + AGN model of Labbe et al. (2024), but with an even steeper dust law (see Section 6.1). All four models favour a massive post-starburst solution, with a very steep dust attenuation law and high optical depth. However, even with such extreme dust, none of these models can produce the strong Balmer break and shape of the rest-frame optical SED, as is evident from the systematic (and significant) features in the residuals blueward and redward of the Balmer break.