Special relativity with a discrete spectrum of singular velocities

The introduction of real transformation formulae containing a whole discrete spectrum of singularities is suggested. Some phenomenological hypotheses are introduced and the group property is substituted by weaker conditions. The first singular speed (c1=c) is invariant with respect to the measures of it from subluminal frames, but the remaining speeds are not invariant. The proposed transformations do not form a closed set (for the superluminal speeds) and, therefore, the problem of having (within this framework) a principle of relativity valid for any velocity remains open