  The first heavy fermion superconductor CeCu$_2$Si$_2$ 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 $7 \text{GPa}$ on a high quality CeCu$_2$Si$_2$
single crystal. Reliable resistivity data reveal for the first time a scaling
behavior close to the supposed valence transition, and allow to locate the
critical end point at $4.5\pm0.2 \text{GPa}$ and a slightly negative
temperature. In the same pressure region, remarkable features have also been
detected in the other physical properties, acting as further signatures of the
Ce valence crossover and the associated critical fluctuations.
