Aims. We aim to refine the fundamental parameters of the TOI-2141 planetary system, which includes a transiting sub-Neptune orbiting a Sun-like star on a relatively long orbit of 18.26 days, by combining new photometric and spectroscopic observations. Methods. We analyzed new space-based photometry from TESS and CHEOPS, as well as 61 radial velocity measurements from HARPS-N. We performed individual and joint photometric and RV analyses using several modeling tools within a Bayesian model comparison framework. Results. We refined the radius and mass of the transiting planet TOI-2141 b to 3.15 ± 0.04 R⊕ and 20.1 ± 1.6 M⊕ to levels that are five and two times more precise, respectively, than the previously reported values. Our radial velocity analysis reveals two additional non-transiting companions with orbital periods of 5.46 and 60.45 days. Despite the innermost planet's high geometric transit probability, we found no evidence of transits in the photometric data. Conclusions. The bulk properties of TOI-2141 b suggest a significant volatile envelope atop an Earth-like core. The modeling indicates a hydrogen-rich atmosphere that could have experienced mild photoevaporation over the system's history. Planets b and c are believed to exhibit a modest mutual inclination of at least ~2.4°.