  Pure massive gravity is strongly coupled at a certain low scale, known as
Lambda_3. I show that the theory can be embedded into another one, with new
light degrees of freedom, to increase the strong scale to a significantly
larger value. Certain universal aspects of the proposed mechanism are
discussed, notably that the coupling of the longitudinal mode to a
stress-tensor is suppressed, thus making the linear theory consistent with the
fifth-force exclusion. An example of the embedding theory studied in detail is
5D AdS massive gravity, with a large cosmological constant. In this example the
4D strong scale can be increased by 19 orders of magnitude. Holographic duality
then suggests that the strong scale of the 4D massive gravity can be increased
by coupling it to a 4D non-local CFT, endowed with a UV cutoff; however, the 5D
classical gravity picture appears to be more tractable.
