Standard Model fails to explain neutrino oscillations, dark matter, and baryon asymmetry of the Universe. All these problems can be solved with three sterile neutrinos added to SM. Quite remarkably, if sterile neutrino masses are well below the electroweak scale, this modification-Neutrino Minimal Standard Model (nu MSM)-can be tested experimentally. We discuss a new experiment on search for decays of GeV-scale sterile neutrinos, which are responsible for the matter-antimatter asymmetry generation and for the active neutrino masses. If lighter than 2 GeV, these particles can be produced in decays of charm mesons generated by high energy protons in a target, and subsequently decay into SM particles. To fully explore this sector of nu MSM, the new experiment requires data obtained with at least 10(20) incident protons on target (achievable at CERN SPS in future) and a big volume detector constructed from a large amount of identical single modules, with a total sterile neutrino decay length of few kilometers. The preliminary feasibility study for the proposed experiment shows that it has sensitivity which may either lead to the discovery of new particles below the Fermi scale-right-handed partners of neutrinos-or rule out seesaw sterile neutrinos with masses below 2 GeV.