  We show how a deformed composition law of four-momenta can be used to define,
at the classical level, a modified notion of spacetime for a system of two
particles through the crossing of worldlines in particle interactions. We
present a derivation of a generic relativistic isotropic deformed kinematics
and discuss the complementarity and relations with other derivations based on
$\kappa$-Poincar\'e Hopf algebra or on the geometry of a maximally symmetric
momentum space.
