  We construct a Lorentz invariant massive particle model in (2+1) space-time
with an enlarged set of symmetries which includes Bondi-Metzner-Sachs (BMS)
translations (supertranslations), using the non-linear realization framework.
The Hamiltonian formalism for the resulting Lagrangian is constructed, and the
infinite phase-space constraints and the set of gauge transformations are
analysed. We also compute the massless limit of the theory in phase-space.
After eliminating the gauge degrees of freedom, the physical reduced space is
left only with the degrees of freedom of a standard Poincar\'e particle but
with a residual set of symmetries that we prove to be BMS. A similar result for
the massless limit, including in this case superrotations, is pointed out.
