  In this work we report the independent discovery and analysis of nine new
compact triply eclipsing triple star systems found with the TESS mission: TICs
47151245, 81525800, 99013269, 229785001, 276162169, 280883908, 294803663,
332521671, and 356324779. Each of these nine systems exhibits distinct
third-body eclipses where the third (`tertiary') star occults the inner
eclipsing binary (EB), or vice versa. We utilize a photodynamical analysis of
the TESS photometry, archival photometric data, TESS eclipse timing variations
of the EBs, available archival spectral energy distribution curves (SED), and,
in some cases, newly acquired radial velocity observations, to solve for the
parameters of all three stars, as well as most of the orbital elements. From
these analyses we find that the outer orbits of all nine systems are viewed
nearly edge on (i.e., within $\lesssim 4^\circ$), and 6 of the systems are
coplanar to within $5^\circ$; the others have mutual inclination angles of
$20^\circ$, $41^\circ$, and possibly $179^\circ$ (i.e., a retrograde outer
orbit). The outer orbital periods range from 47.8 days to 604 days, with
eccentricities spanning 0.004 to 0.61. The masses of all 18 EB stars are in the
range of 0.9-2.6 M$_\odot$ and are mostly situated near the main sequence. By
contrast, the masses and radii of the tertiary stars range from 1.4-2.8
M$_\odot$ and 1.5-13 R$_\odot$, respectively. We make use of the system
parameters from these 9 systems, plus those from a comparable number of compact
triply eclipsing triples published previously, to gain some statistical insight
into their properties.
