  Demanding the existence of a simple holographic $c$-theorem, it is shown that
a general (parity preserving) theory of gravity in 2+1 dimensions involving
upto four derivative curvature invariants reduces to the new massive gravity
theory. We consider extending the theory including upto six derivative
curvature invariants. Black hole solutions are presented and consistency with
1+1 CFTs is checked. We present evidence that bulk unitarity is still in
conflict with a positive CFT central charge for generic choice of parameters.
However, for a special choice of parameters appearing in the four and six
derivative terms reduces the linearized equations to be two derivative, thereby
ameliorating the unitarity problem.
