The two most successful planet detection techniques, transits and radial velocities, are primarily sensitive to close-in exoplanets. The available statistics for close-in exoplanets is nearly an order of magnitude richer than that of exoplanets on distant orbits, implying that there is still a huge lack of data for determining the occurrence rate of planetary systems with a large orbital-separation hierarchy or similar to that of the Solar System. Other techniques, such as astrometry and microlensing, are more efficient in detecting these planetary systems, but they cannot characterize them to the same extent as transiting planets. Our intent is to study transiting planetary systems composed of at least two gas giants on orbits with a periodicity that goes from one similar to that of Mercury to that of Neptune. We identified a short list of such known and candidate planetary systems that we want to monitor with high-resolution spectrographs. The aim is to confirm the planetary nature of these planetary candidates and determine/refine their masses. The investigation of the atmospheres of cold Jupiters in the future requires a precise measurement of their masses.