  We present a study of the M dwarf exoplanetary systems forthcoming from
NASA's TESS mission. While the mission's footprint is too complex to be
characterized by a single detection completeness, we extract an ensemble
completeness function that recovers the M dwarf planet detections from previous
work. We employ this completeness function, together with a dual-population
planet occurrence model that includes compact multiple planetary systems, to
infer anew the planet yield. We predict both the number of M dwarf planets
likely from TESS and their system architectures. We report four main findings:
first, that TESS will likely detect more planets orbiting M dwarfs that
previously predicted. Around stars with spectral types between M1V--M4V, we
predict TESS will find 990$\pm$350 planets orbiting 715$\pm$255 stars, a
1.5-fold increase over previous predictions. Secondly, TESS will find two or
more transiting planets around 20% of these host stars, a number similar to the
multiplicity yield of NASA's Kepler mission. Thirdly, TESS light curves in
which one or more planets are detected will often contain transits of
additional planets below the detection threshold of TESS. Among a typical set
of 200 TESS hosts to one or more detected planets, 116$\pm$28 transiting
planets will be missed. Transit follow-up efforts with the photometric
sensitivity to detect an Earth or larger around a mid-M dwarf, even with very
modest period completeness, will readily result in additional planet
discoveries. And fourth, the strong preference of TESS for systems of compact
multiples indicates that TESS planets will be dynamically cooler on average
than Kepler planets, with 90% of TESS-detected planets residing in orbits with
$e<0.15$.
