Relativistic deformed kinematics leads to a loss of the absolute locality of interactions. In previous studies, some models of noncommutative spacetimes in a two-particle system that implements locality were considered. In this work (arXiv:2504.03378), we present a characterization of the Lie-Poisson algebras formed by the noncommutative space-time coordinates of a multi-particle system and Lorentz generators as a possible restriction on these models. The relativistic deformed kinematics derived from these algebras are also discussed. Finally, we show its connection with cotangent bundle geometries.