In this paper, we discuss the possibilities offered to neutrino physics by the upgrades of the CERN accelerator complex. Emphasis is on the physics reach of a medium $gamma$ (350-580) $beta$-beam that fully exploits the improvements in the CERN accelerator complex for the luminosity/energy upgrade of the LHC. We show that, this design not only profits of the ongoing efforts for the upgrades of the LHC, but also leverage out the existing infrastructures of the LNGS underground laboratory. Furthermore, given the involved high neutrino energies, above 1 GeV, a non-magnetized iron detector could efficiently exploit the neutrino beam. We show that the performance of this complex for what concerns the discovery of the CP violation in the leptonic sector, in case $theta_{13}$ is discovered by Phase I experiments, is comparable with the current baseline design based on a gigantic water Cherenkov at Frejus. Furthermore, this complex has also some sensitivity to the neutrino mass hierarchy.
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