  GR can be interpreted as a theory of evolving 3-geometries. A recent such
formulation, the 3-space approach of Barbour, Foster and \'{O} Murchadha, also
permits the construction of a limited number of other theories of evolving
3-geometries, including conformal gravity and strong gravity. In this paper, we
use the 3-space approach to construct a 1-parameter family of theories which
generalize strong gravity. The usual strong gravity is the strong-coupled limit
of GR, which is appropriate near singularities and is one of very few regimes
of GR which is amenable to quantization. Our new strong gravity theories are
similar limits of scalar-tensor theories such as Brans--Dicke theory, and are
likewise appropriate near singularities. They represent an extension of the
regime amenable to quantization, which furthermore spans two qualitatively
different types of inner product.
  We find that strong gravity theories permit coupling only to ultralocal
matter fields and that they prevent gauge theory. Thus in the classical
picture, gauge theory breaks down (rather than undergoing unification) as one
approaches the GR initial singularity.
