  Cavity QED with cooperativity far greater than unity enables high-fidelity
quantum sensing and information processing. The high-cooperativity regime is
often reached through the use of short, single-mode resonators. More
complicated multimode resonators, such as the near-confocal optical
Fabry-P\'{e}rot cavity, can provide intracavity atomic imaging in addition to
high cooperativity. This capability has recently proved important for exploring
quantum many-body physics in the driven-dissipative setting. In this work, we
show that a confocal cavity QED microscope can realize cooperativity in excess
of 110. This cooperativity is on par with the very best single-mode cavities
(which are far shorter) and 21$\times$ greater than single-mode resonators of
similar length and mirror radii. The 1.7-$\mu$m imaging resolution is naturally
identical to the photon-mediated interaction range. We measure these quantities
by determining the threshold of cavity superradiance when small, optically
tweezed Bose-Einstein condensates are pumped at various intracavity locations.
Transmission measurements of an ex situ cavity corroborate these results. We
provide a theoretical description that shows how cooperativity enhancement
arises from the dispersive coupling to the atoms of many near-degenerate modes.
