I will present results from a Doppler survey carried out with HARPS, FEROS and CARMENES for a sample of 45 stars, which were previously reported to have a single planetary companion in orbit. Most of these planetary discoveries were announced based on sparse radial velocity (RV) data samples, insufficient precision and sometimes incomplete phase coverage. Our survey aims to increase the observational efforts for these targets in an attempt to detect additional planets. So far, almost half of our targets are already showing strong indications of additional companions. For these systems with additional companions, we have conducted detailed statistical and dynamical analyses of the RV data and studied the long-term stability. We have a strong reason to believe that a significant fraction of the "single" RV planets are in fact either pairs of low-eccentricity near-resonant planets misinterpreted as a single planet or systems with a long-period massive companion, which can be revealed only by increasing the long temporal baseline of the observations. Since multiple planet systems (and their dynamical architecture) are important for probing planetary formation and evolution scenarios, I will emphasize the importance of further follow-up of RV planet hosts.