  We propose new massive gravity theories with 5 dynamical degrees of freedom.
We evade uniqueness theorems regarding the form of the kinetic and potential
terms by adopting the "generalized massive gravity" framework, where a global
translation invariance is broken. By exploiting the rotation symmetry in the
field space, we determine two novel classes of theories. The first one is an
extension of generalized massive gravity with a non-minimal coupling. On the
other hand, the second theory produces a mass term that is different from de
Rham, Gabadadze, Tolley construction and trivially has 5 degrees of freedom.
Both theories allows for stable cosmological solutions without infinite strong
coupling, which are free of ghost and gradient instabilities.
