  Multi-planet systems are valuable arenas for investigating exoplanet
architectures and comparing planetary siblings. TOI-1246 is one such system,
with a moderately bright K dwarf ($\rm{V=11.6,~K=9.9}$) and four transiting
sub-Neptunes identified by TESS with orbital periods of
$4.31~\rm{d},~5.90~\rm{d},~18.66~\rm{d}$, and $~37.92~\rm{d}$. We collected 130
radial velocity observations with Keck/HIRES and TNG/HARPS-N to measure planet
masses. We refit the 14 sectors of TESS photometry to refine planet radii
($\rm{2.97 \pm 0.06~R_\oplus},\rm{2.47 \pm 0.08~R_\oplus}, \rm{3.46 \pm
0.09~R_\oplus}$, $\rm{3.72 \pm 0.16~R_\oplus}$), and confirm the four planets.
We find that TOI-1246 e is substantially more massive than the three inner
planets ($\rm{8.1 \pm 1.1 M_\oplus}$, $\rm{8.8 \pm 1.2 M_\oplus}$, $\rm{5.3 \pm
1.7 M_\oplus}$, $\rm{14.8 \pm 2.3 M_\oplus}$). The two outer planets, TOI-1246
d and TOI-1246 e, lie near to the 2:1 resonance ($\rm{P_{e}/P_{d}=2.03}$) and
exhibit transit timing variations. TOI-1246 is one of the brightest four-planet
systems, making it amenable for continued observations. It is one of only six
systems with measured masses and radii for all four transiting planets. The
planet densities range from $\rm{0.70 \pm 0.24}$ to $3.21 \pm 0.44
\rm{g/cm^3}$, implying a range of bulk and atmospheric compositions. We also
report a fifth planet candidate found in the RV data with a minimum mass of
25.6 $\pm$ 3.6 $\rm{M_\oplus}$. This planet candidate is exterior to TOI-1246 e
with a candidate period of 93.8 d, and we discuss the implications if it is
confirmed to be planetary in nature.
