In multiple-planet systems, gravitational interactions of exoplanets could lead to transit timing variations (TTVs), whose amplitude becomes significantly enhanced when planets are in or near mean-motion resonances (MMRs), making them more easily detectable. In cases where both TTVs and radial velocity (RV) measurements are available, combined analysis can break degeneracies and provide robust planetary and system characterization, even detecting non-transiting planets. In this context, HIP 41378 hosts five confirmed transiting planets with periods ranging from 15 to over 542 days, providing a unique dynamical laboratory for investigating wide multi-planet systems analogous to the Solar System. In this study, we present an intensive space-based photometric follow-up of HIP 41378, combining 15 new CHEOPS observations with eight TESS sectors, alongside data from K2, Spitzer, HST, and 311 HARPS spectra. We dynamically modeled the TTVs and RV signals of the two inner sub-Neptunes via N-body integration. These planets, HIP 41378 b (Pb = 15.57 days, Rb = 2.45 R⊕) and HIP 41378 c (Pc = 31.71 days, Rc = 2.57 R⊕), are close to (∆ ~ 1.8%) a 2:1 period commensurability. We report a clear detection of TTVs with amplitudes of 20 minutes for planet b and greater than 3 hours for planet c. We dynamically confirm the planetary nature of HIP 41378 g, a non-transiting planet with a period of about 64 days and a mass of about 7 M⊕, close to a 2:1 commensurability with planet c, suggesting a possible mean-motion resonance chain in the inner system. Our precise determination of the masses, eccentricities, and radii of HIP 41378 b and c enabled us to investigate their possible volatile-rich compositions. Finally, by leveraging on the last TESS sectors we constrained the period of HIP 41378 d to three possible aliases (Pd = 278, 371, and 1113 days) suggesting that the system could be placed in a double quasi resonant chain, highlighting its complex dynamical architecture.
