  This paper reports on the detailed characterisation of the K2-111 planetary
system with K2, WASP, and ASAS-SN photometry as well as high-resolution
spectroscopic data from HARPS-N and ESPRESSO. The host, K2-111, is confirmed to
be a mildly evolved ($\log g=4.17$), iron-poor ([Fe/H]$=-0.46$), but
alpha-enhanced ([$\alpha$/Fe]$=0.27$), chromospherically quiet, very old thick
disc G2 star. A global fit, performed by using PyORBIT shows that the
transiting planet, K2-111b, orbits with a period $P_b=5.3518\pm0.0004$ d, and
has a planet radius of $1.82^{+0.11}_{-0.09}$ R$_\oplus$ and a mass of
$5.29^{+0.76}_{-0.77}$ M$_\oplus$, resulting in a bulk density slightly lower
than that of the Earth. The stellar chemical composition and the planet
properties are consistent with K2-111b being a terrestrial planet with an iron
core mass fraction lower than the Earth. We announce the existence of a second
signal in the radial velocity data that we attribute to a non-transiting
planet, K2-111c, with an orbital period of $15.6785\pm 0.0064$ days, orbiting
in near-3:1 mean-motion resonance with the transiting planet, and a minimum
planet mass of $11.3\pm1.1$ M$_\oplus$. Both planet signals are independently
detected in the HARPS-N and ESPRESSO data when fitted separately. There are
potentially more planets in this resonant system, but more well-sampled data
are required to confirm their presence and physical parameters.
