  We report the Transiting Exoplanet Survey Satellite ($TESS$) detection of a
multi-planet system orbiting the $V=10.9$ K0 dwarf TOI 125. We find evidence
for up to five planets, with varying confidence. Three high signal-to-noise
transit signals correspond to sub-Neptune-sized planets ($2.76$, $2.79$, and
$2.94\ R_{\oplus}$), and we statistically validate the planetary nature of the
two inner planets ($P_b = 4.65$ days, $P_c = 9.15$ days). With only two
transits observed, we report the outer object ($P_{.03} = 19.98$ days) as a
high signal-to-noise ratio planet candidate. We also detect a candidate
transiting super-Earth ($1.4\ R_{\oplus}$) with an orbital period of only
$12.7$ hours and a candidate Neptune-sized planet ($4.2\ R_{\oplus}$) with a
period of $13.28$ days, both at low signal-to-noise. This system is amenable to
mass determination via radial velocities and transit timing variations, and
provides an opportunity to study planets of similar size while controlling for
age and environment. The ratio of orbital periods between TOI 125 b and c
($P_c/P_b = 1.97$) is slightly smaller than an exact 2:1 commensurability and
is atypical of multiple planet systems from $Kepler$, which show a preference
for period ratios just $wide$ of first-order period ratios. A dynamical
analysis refines the allowed parameter space through stability arguments and
suggests that, despite the nearly commensurate periods, the system is unlikely
to be in resonance.
