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.