It's still an exotic model, but if there's an extra dimension that light can fit into - even a tiny loop that it just spirals around as it propagates - then it'

It's still an exotic model, but if there's an extra dimension that light can fit into - even a tiny loop that it just spirals around as it propagates - then it's possible that at higher energy densities, it spirals at a shallower angle. That would make it appear to propagate through the three normal spatial dimensions faster even if it has the same speed across all four dimensions. João Magueijo wrote an approachable book on this called "Faster than the Speed of Light: The Story of a Scientific Speculation".