The NUMEN project aims at accessing experimentally driven information on Nuclear Matrix Elements (NME) involved in the half-life of the neutrinoless double beta decay (0v beta beta), by high-accuracy measurements of Heavy Ion (HI) induced Double Charge Exchange (DCE) reaction cross sections. In particular, the (O-18,Ne-18) and (Ne-20, O-20) reactions are used as tools for beta(+)beta(+) and beta(-)beta(-) decays, respectively. In the experiments, performed at INFN - Laboratory Nazionali del Sud (LNS) in Catania, the beams are accelerated by the Superconducting Cyclotron (CS) and the reaction ejectiles are detected the MAGNEX magnetic spectrometer. The measured cross sections are challengingly low (a few nb), being the total reaction cross section much larger (a few b), thus a high sensitivity and a large rejection capability are demanded to the experimental set-up. This limits the present exploration to few selected isotopes of interest in the context of typically low-yield experimental runs. A major upgrade of the LNS facility is foreseen in order to increase the experimental yield of at least two orders of magnitude, still keeping the high sensitivity of the present set-up, making it feasible a systematic study of all the cases of interest. Frontiers technologies are going to be developed, to this purpose, for the accelerator and the detection systems. In parallel, advanced theoretical models are being developed in order to extract the nuclear structure information from the measured cross sections.