  UV-FIR SED modeling is an effective way to disentangle emission between star
formation (SF) and active galactic nuclei (AGN) in galaxies; however, this
approach becomes uncertain for composite AGN/SF galaxies that comprise 50-70%
of IR-samples. Cosmic X-ray background (XRB) models require a large fraction of
obscured AGN to reproduce the observed XRB peak, motivating reliable SED
analyses in objects where the AGN may be ``buried" in the galaxy and in the
mid-IR to far-IR SED. In this paper, we study a 24$\mu$m-selected ($S_{24}$ >
100$\mu$Jy) sample of 95 galaxies with $0 \% < f_{MIR,AGN} < 100 \%$, 0.4 < z <
2.7, and $10^{11}$L$_{\odot}$ < L$_{IR}$ < $10^{13}$L$_{\odot}$. We test the
performance of AGN models ranging in torus optical depth via SED fitting,
comparing results with Spitzer MIR spectroscopy and X-ray observations.
Best-fit torus optical depth can shed light on whether these galaxies host a
luminous obscured AGN population. We find that permitting a broader AGN SED
parameter space results in improved fit quality with higher optical depths,
higher FIR AGN contributions, and higher $L_{Bol}$, impacting the bright-end of
the $L_{Bol}$ luminosity function. Our results suggest there may be a
population of dust-obscured composites that are bolometrically significant but
have their AGN mostly hidden in the mid-IR SED. If so, literature applications
of SED fitting that often simplify AGN models or omit optically thick tori may
largely underestimate AGN contribution from composite sources, as these sources
are both numerous and have solutions sensitive to the assumed range of AGN
models.
