Could a more prosaic explanation just be that the speed-of-light limit still holds, but we just got the speed wrong? The fundamental limit is to the speed of light in a vacuum. This has been measured extremely accurately.
But, we know space is not a vacuum. Maybe we've been actually measuring the speed of light in a vacuum energy field instead, and the neutrinos measure by CERN are actually travelling closer to the true "speed of light in a vacuum".
Of course, there are other tests of the value of "c", such as the equivalence of mass and energy, but there appears to be some wriggle room in the experimental tests of this.
PS: This is almost definitely complete nonsense, probably for various reasons, but for a start the neutrino measurements for SN1987A would have to be bogus.
PS: This is almost definitely complete nonsense, probably for various reasons, but for a start the neutrino measurements for SN1987A would have to be bogus.