The goal of NUMEN project is to access experimentally driven information on Nuclear Matrix Elements (NME) involved in the neutrinoless double beta decay (0νββ), by high-accuracy measurements of the cross sections of Heavy Ion (HI) induced Double Charge Exchange (DCE) reactions. The knowledge of the nuclear matrix elements is crucial to infer the neutrino average masses from the possible measurement of the half-life of 00νββ decay and to compare experiments on different isotopes. In particular, the (¹⁸O, ¹⁸Ne) and (²⁰Ne, ²⁰O) reactions are performed as tools for β⁺β⁺ and β^-β^- decays, respectively. The experiments are performed at INFN - Laboratory Nazionali del Sud (LNS) in Catania using the Superconducting Cyclotron (CS) to accelerate the beams and the MAGNEX magnetic spectrometer to detect the reaction products. The measured cross sections are very low, limiting the present exploration to few selected isotopes of interest in the context of typically low-yield experimental runs. In order to make feasible a systematic study of all the candidate nuclei, a major upgrade of the LNS facility is foreseen to increase the experimental yield of about two orders of magnitude. To this purpose, frontier technologies are going to be developed for both the accelerator and the detection systems. In parallel, advanced theoretical models will be developed to extract the nuclear structure information from the measured cross sections.