Lets suppose that neutrinos do travel faster than light.
This need not require any change to Relativity.
From the point of view of Relativity it would just mean the neutrinos need to be regarded as traveling backwards in time. Traveling backwards in time is not ruled by Relativity. Indeed Relativity requires that any conjectured FTL particles be deemed as traveling backwards in time.
There are two possible ways that FTL particles can do this without requiring any change to Relativity. However one way would violate intuitive causality rules. The other way wouldn't. The way which violates causality rules is if the neutrinos traveled back in time (by 60 nanoseconds) at the exact moment they were emitted. In this scenario, for the remainder of their flight, they would be traveling at the speed limit c. But if they had traveled back in time at the moment of emission this would result in violations of causality, be falsifiable, and/or violate the experimenter's sanity.
The other way is that FTL particles travel back in time, but over time. In this scenario, at the point of emission, the 'distance' traveled back in time is exactly zero, but over the duration of the flight, the 'distance' traveled back in time increases so that by the time it is observed it has traveled back in time by the observed 60 nanoseconds. This scenario doesn't violate causality rules.
Relativity doesn't rule out FTL particles. It is only non-time-travel rules that would rule such out, but there are no non-time-travel rules I've come across in theoretical physics. There are only informal conjectures at such.
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Recent tests on CERN equipment for measuring neutrino flight have identified a faulty cable with an interesting result - that the cable was found to introduce a 60 nanosecond error in the information it was otherwise mediating. Nobody seems to be saying much of anything else other than noting this fault - leaving it up to us to draw our own conclusions. A far cry from the original proposal, where conclusions were enthusiastically postulated: that neutrinos appeared to be travelling faster than light.
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