  Planets in binary systems are a fascinating and yet poorly understood
phenomenon. Since there are only a few known large-separation systems in which
both components host planets, characterizing them is a key target for planetary
science. In this paper, we aim to carry out an exhaustive analysis of the
interesting XO-2 system, where one component appears to be a system with only
one planet, while the other has at least three planets. Over the last 9 years,
we have collected 39 spectra of XO-2N and 106 spectra of XO-2S with the High
Accuracy Radial velocity Planet Searcher for the Northern emisphere (HARPS-N)
in the framework of the Global Architecture of Planetary Systems project, from
which we derived precise radial velocity and activity indicator measurements.
Additional spectroscopic data from the High Resolution Echelle Spectrometer and
from the High Dispersion Spectrograph, and the older HARPS-N data presented in
previous papers, have also been used to increase the total time span. We also
used photometric data from TESS to search for potential transits that have not
been detected yet. For our analysis, we mainly used PyORBIT, an advanced Python
tool for the Bayesian analysis of RVs, activity indicators, and light curves.
We found evidence for an additional long-period planet around XO-2S and
characterized the activity cycle likely responsible for the long-term RV trend
noticed for XO-2N. The new candidate is an example of a Jovian analog with
$m\sin i \sim 3.7$ M$_J$, $a \sim 5.5$ au, and $e = 0.09$. We also analyzed the
stability and detection limits to get some hints about the possible presence of
additional planets. Our results show that the planetary system of XO-2S is at
least one order of magnitude more massive than that of XO-2N. The implications
of these findings for the interpretation of the previously known abundance
difference between components are also discussed.
