  We construct a class of theories which extend New Massive Gravity to higher
orders in curvature in any dimension. The lagrangians arise as limits of a new
class of bimetric theories of Lovelock gravity, which are unitary theories free
from the Boulware-Deser ghost. These Lovelock bigravity models represent the
most general non-chiral ghost-free theories of an interacting massless and
massive spin-two field in any dimension. The scaling limit is taken in such a
way that unitarity is explicitly broken, but the Boulware-Deser ghost remains
absent. This automatically implies the existence of a holographic $c$-theorem
for these theories. We also show that the Born-Infeld extension of New Massive
Gravity falls into our class of models demonstrating that this theory is also
free of the Boulware-Deser ghost. These results extend existing connections
between New Massive Gravity, bigravity theories, Galileon theories and
holographic $c$-theorems.
