  The first wave of observations with JWST has revealed a striking
overabundance of luminous galaxies at early times ($z>10$) compared to models
of galaxies calibrated to pre-JWST data. Early observations have also uncovered
a large population of supermassive black holes (SMBHs) at $z>6$. Because many
of the high-$z$ objects appear extended, the contribution of active galactic
nuclei (AGNs) to the total luminosity has been assumed to be negligible. In
this work, we use a semi-empirical model for assigning AGNs to galaxies to show
that active galaxies can boost the stellar luminosity function (LF) enough to
solve the overabundance problem while simultaneously remaining consistent with
the observed morphologies of high-$z$ sources. We construct a model for the
composite AGN+galaxy LF by connecting dark matter halo masses to galaxy and
SMBH masses and luminosities, accounting for dispersion in the mapping between
host galaxy and SMBH mass and luminosity. By calibrating the model parameters
-- which characterize the $M_\bullet-M_\star$ relation -- to a compilation of
$z>10$ JWST UVLF data, we show that AGN emission can account for the excess
luminosity under a variety of scenarios, including one where 10\% of galaxies
host BHs of comparable luminosities to their stellar components. Using a sample
of simulated objects and real observations, we demonstrate that such
low-luminosity AGNs can be `hidden' in their host galaxies and be missed in
common morphological analyses. We find that for this explanation to be viable,
our model requires a population of BHs that are overmassive
($M_\bullet/M_\star\sim10^{-2}$) with respect to their host galaxies compared
to the local relation and are more consistent with the observed relation at
$z=4-8$. We explore the implications of this model for BH seed properties and
comment on observational diagnostics necessary to further investigate this
explanation.
