  In order to understand the observed physical and orbital diversity of
extrasolar planetary systems, a full investigation of these objects and of
their host stars is necessary. Within this field, one of the main purposes of
the GAPS observing project with HARPS-N@TNG is to provide a more detailed
characterisation of already known systems. In this framework we monitored the
star, hosting two giant planets, HD108874, with HARPS-N for three years in
order to refine the orbits, to improve the dynamical study and to search for
additional low-mass planets in close orbits. We subtracted the radial velocity
(RV) signal due to the known outer planets, finding a clear modulation of 40.2
d period. We analysed the correlation between RV residuals and the activity
indicators and modelled the magnetic activity with a dedicated code. Our
analysis suggests that the 40.2 d periodicity is a signature of the rotation
period of the star. A refined orbital solution is provided, revealing that the
system is close to a mean motion resonance of about 9:2, in a stable
configuration over 1 Gyr. Stable orbits for low-mass planets are limited to
regions very close to the star or far from it. Our data exclude super-Earths
with Msin i \gtrsim 5 M_Earth within 0.4 AU and objects with Msin i \gtrsim 2
M_Earth with orbital periods of a few days. Finally we put constraints on the
habitable zone of the system, assuming the presence of an exomoon orbiting the
inner giant planet.
