  The determination of the missing $U_{e3}$ element (magnitude and phase) of
the PMNS neutrino mixing matrix is possible via the detection of $\numu\to\nue$
oscillations at a baseline $L$ and energy $E$ given by the atmospheric
observations, corresponding to a mass squared difference $E/L \sim \Delta
m^2\simeq 2.5\times 10^{-3} eV^2$. While the current optimization of the CNGS
beam provides limited sensitivity to this reaction, we discuss in this document
the physics potential of an intensity upgraded and energy re-optimized CNGS
neutrino beam coupled to an off-axis detector. We show that improvements in
sensitivity to $\theta_{13}$ compared to that of T2K and NoVA are possible with
a next generation large liquid Argon TPC detector located at an off-axis
position (position rather distant from LNGS, possibly at shallow depth). We
also address the possibility to discover CP-violation and disentangle the mass
hierarchy via matter effects. The considered intensity enhancement of the CERN
SPS has strong synergies with the upgrade/replacement of the elements of its
injector chain (Linac, PSB, PS) and the refurbishing of its own elements,
envisioned for an optimal and/or upgraded LHC luminosity programme.
