  Detached eclipsing binaries are the primary tool used to measure precise
masses and radii of stars. In our previous paper estimating the parameters of
more than 30,000 detached eclipsing binaries, we identified 766 eclipsing
binaries with additional features in their All-Sky Automated Survey for
Supernovae (ASAS-SN) and Transiting Exoplanet Survey Satellite (TESS) light
curves. Here, we characterize these "extra-physics" systems, identifying
eclipsing binaries with spotted stars, pulsating components, and candidate
triple/quadruple systems. We use the Gaia, ATLAS, ZTF, and ASAS-SN variable
star catalogs to consider possible blends. We use MIST isochrones and
evolutionary tracks to identify systems with main sequence, subgiant, and giant
primaries and highlight systems in sparsely populated regions of the
color-magnitude diagram. We find that the orbital period distribution of
spotted binaries is divided by evolutionary state and find 68 with X-ray
detections. For the candidate triple/quadruples and pulsating systems, we
calculate the extra orbital/pulsational period and identify systems with
resonances. Finally, we highlight a number of exotic systems, including
eclipsing CVs, subdwarfs, and binaries with disks.
