  We propose a general framework to describe Planckian deviations from Special
Relativity (SR) compatible with a relativistic principle. They are introduced
as the leading corrections in an asymptotic approach to SR going beyond the
energy power expansion of effective field theories. We discuss the conditions
in which these Planckian effects might be experimentally observable in the near
future, together with the non-trivial limits of applicability of this
asymptotic approach that such a situation would produce, both at the very high
(ultraviolet) and the very low (infrared) energy regimes.
