  We report the confirmation of three exoplanets transiting TOI-4010
(TIC-352682207), a metal-rich K dwarf observed by TESS in Sectors 24, 25, 52,
and 58. We confirm these planets with HARPS-N radial velocity observations and
measure their masses with 8 - 12% precision. TOI-4010 b is a sub-Neptune ($P =
1.3$ days, $R_{p} = 3.02_{-0.08}^{+0.08}~R_{\oplus}$, $M_{p} =
11.00_{-1.27}^{+1.29}~M_{\oplus}$) in the hot Neptune desert, and is one of the
few such planets with known companions. Meanwhile, TOI-4010 c ($P = 5.4$ days,
$R_{p} = 5.93_{-0.12}^{+0.11}~R_{\oplus}$, $M_{p} =
20.31_{-2.11}^{+2.13}~M_{\oplus}$) and TOI-4010 d ($P = 14.7$ days, $R_{p} =
6.18_{-0.14}^{+0.15}~R_{\oplus}$, $M_{p} = 38.15_{-3.22}^{+3.27}~M_{\oplus}$)
are similarly-sized sub-Saturns on short-period orbits. Radial velocity
observations also reveal a super-Jupiter-mass companion called TOI-4010 e in a
long-period, eccentric orbit ($P \sim 762$ days and $e \sim 0.26$ based on
available observations). TOI-4010 is one of the few systems with multiple
short-period sub-Saturns to be discovered so far.
