The first heavy fermion superconductor CeCu2Si2 has not revealed all its striking mysteries yet. At high pressures, superconductivity is supposed to be mediated by valence fluctuations, in contrast to ambient pressure, where spin fluctuations most likely act as pairing glue. We have carried out a multiprobe (electric transport, thermopower, ac specific heat, Hall and Nernst effects) experiment up to 7 GPa on a high-quality CeCu2Si2 single crystal. For the first time, the resistivity data make it possible quantitatively to draw the valence crossover line within the p-T plane and to locate the critical end point at 4.5 ± 0.2 GPa and a slightly negative temperature. In the same pressure region, remarkable features have also been detected in the other physical properties, presumably acting as further signatures of the Ce valence crossover and the associated critical fluctuations: We observe maxima in the Hall and Nernst effects and a sign change and a strong sensitivity on magnetic field in the thermopower signal.