  We investigate the Chern-Simons-like formulation of exotic general massive
gravity models within the framework of third-way to three-dimensional gravity.
We classify our construction into two main approaches: one using torsional
cosmological Einstein and exotic massive gravity equations, and the other a
torsion-free approach. The former approach, while mathematically appealing,
precludes the construction of critical exotic models where the central charges
vanish. In contrast, the latter approach has a wider parameter space and allows
for the construction of critical models. An explicit example of an exotic
general model is provided to illustrate both methods. Our methodology
represents the first step towards establishing the most general
Chern-Simons-like formulation of third-way to three-dimensional gravity, which
would enable the study of identifying its bulk/boundary unitary sector.
