  We followed-up with ESPRESSO the K0V star HIP 29442 (TOI-469), already known
to host a validated sub-Neptune companion TOI-469.01. We aim to verify the
planetary nature of TOI-469.01. We modelled radial velocity and photometric
time series to measure the dynamical mass, radius, and ephemeris, and to
characterise the internal structure and composition of TOI-469.01. We confirmed
the planetary nature of TOI-469.01. Thanks to ESPRESSO we discovered two
additional close-in companions. We also detected their low signal-to-noise
transit signals in the TESS light curve. HIP 29442 is a compact multi-planet
system, and the three planets have orbital periods $P_{\rm orb,
b}=13.63083\pm0.00003$, $P_{\rm orb, c}=3.53796\pm0.00003$, and $P_{\rm orb,
d}=6.42975^{+0.00009}_{-0.00010}$ days, and we measured their masses with high
precision: $m_{\rm p, b}=9.6\pm0.8~M_{\oplus}$, $m_{\rm p,
c}=4.5\pm0.3~M_{\oplus}$, and $m_{\rm p, d}=5.1\pm0.4~M_{\oplus}$. We measured
radii and bulk densities of all the planets (the 3$\sigma$ confidence intervals
are shown in parenthesis): $R_{\rm p, b}=3.48^{+0.07 (+0.19)}_{-0.08 (-0.28)}
~R_{\oplus}$ and $\rho_{\rm p, b}=1.3\pm0.2 (0.3) g~cm^{-3}$; $R_{\rm p,
c}=1.58^{+0.10 (+0.30)}_{-0.11 (-0.34)}~R_{\oplus}$ and $\rho_{\rm p,
c}=6.3^{+1.7 (+6.0)}_{-1.3 (-2.7)} g~cm^{-3}$; $R_{\rm p,
d}=1.37\pm0.11^{(+0.32)}_{(-0.43)}~R_{\oplus}$ and $\rho_{\rm p, d}=11.0^{+3.4
(+21.0)}_{-2.4 (-6.3)} g~cm^{-3}$. We used the more conservative 3$\sigma$
confidence intervals for the radii as input to the interior structure
modelling. We find that HIP 29442 $b$ appears as a typical sub-Neptune, likely
surrounded by a gas layer of pure H-He with a mass of $0.27^{+0.24}_{-0.17}
M_{\oplus}$ and a thickness of $1.4\pm0.5 R_{\oplus}$. For the innermost
companions HIP 29442 $c$ HIP 29442 $d$, the model supports an Earth-like
composition.
