  General exotic bi-gravity, obtained in Ozkan et al. (Phys Rev Lett
123(3):031303, 2019), is a unitary parity-preserving model which describes two
interacting spin-two fields in three-dimensional spacetime. Adopting a
symplectic viewpoint, we investigate the dynamical structure of general exotic
bi-gravity theory. In particular, by exploiting the properties of the
corresponding pre-symplectic matrix and its associated zero-modes, we
explicitly derive all constraints of the theory, including the integrability
conditions and scalar relationships between all the parameters and fields
defining the model. Then, as an application, these scalar relationships are
used for studying the anti-de Sitter background. After that, we derive the
gauge transformations for the dynamical variables from the structure of the
remaining zero-modes, meaning that such zero-modes are indeed the generators of
the gauge symmetry of the theory. Finally, by switching off one of the four
coupling constants $\beta_{n}$ and assuming the invertibility of some of the
dreibeins, we find that the general exotic bi-gravity theory has two physical
degrees of freedom.
