Due to observational biases, a large fraction of known exoplanets are short-period objects. However, the search for planets began more than 20 years ago, so it is already possible, using a proper data set, to start exploring a wider range of the parameter space, i.e., that of long-period planets. This paper aims to investigate the presence of long-period giant companions in two systems where one or more planets are already known and for which a long- term trend in the Radial Velocities (RVs) was noted in previous works. Over the last 11 years, we collected 122 spectra of HD 75898 and 72 spectra of HD 11506 with HARPS-N in the framework of the Global Architecture of Planetary Systems (GAPS) project, from which we derived precise RV and activity indicators measurements. Additional RV data from HIRES have also been used to increase the total time span. For our RV analysis, we used PyORBIT, an advanced Python tool for the simultaneous Bayesian analysis of RVs and stellar activity indicators. In addition, we used astrometric (Gaia DR3) and imaging archive data to complete our analysis. In particular, we combined RVs and astrometry to better constrain the mass and period of the new long-period companions. Results. We found evidence for one additional long-period companion (gas giant planet or brown dwarf) in both systems considered. The new candidate for HD 75898 has a period of roughly 18 yr and a true mass of around 8.5M_J_. For HD 11506, we confirm the new object (planet d) announced by Feng et al. (2022ApJS..262...21F) but we find that the period and true mass are both almost twice compared to their results (P_d_~72yr, M_d_~13M_J_). In addition, for HD 75898, we also found evidence of an activity cycle affecting RVs with a period one order of magnitude lower compared to what was previously found in the literature