  We obtain a new 3D gravity model from two copies of parity-odd
Einstein-Cartan theories. Using Hamiltonian analysis, we demonstrate that the
only local degrees of freedom are two massive spin-2 modes. Unitarity of the
model in anti-de Sitter and Minkowski backgrounds can be satisfied for vast
choices of the parameters without fine-tuning. The recent "exotic massive 3D
gravity" model arises as a limiting case of the new model. We also show that
there exist trajectories on the parameter space of the new model which cross
the boundary between unitary and non-unitary regions. At the crossing point,
one massive graviton decouples resulting in a unitary model with just one bulk
degree of freedom but two positive central charges at odds with the usual
expectation that the critical model has at least one vanishing central charge.
Given the fact that a suitable non-relativistic version of bi-gravity has been
used as an effective theory for gapped spin-2 fractional quantum Hall states,
our model may have interesting applications in condensed matter physics.

High Energy Physics - Theory;General Relativity and Quantum Cosmology