  We derive the low-energy effective theory of gravity for a generalized
Randall-Sundrum scenario, allowing for a third self-gravitating brane to live
in the 5D bulk spacetime. At zero order the 5D spacetime is composed of two
slices of anti-de Sitter spacetime, each with a different curvature scale, and
the 5D Weyl tensor vanishes. Two boundary branes are at the fixed points of the
orbifold whereas the third brane is free to move in the bulk. At first order,
the third brane breaks the otherwise continuous evolution of the projection of
the Weyl tensor normal to the branes. We derive a junction condition for the
projected Weyl tensor across the bulk brane, and combining this constraint with
the junction condition for the extrinsic curvature tensor, allows us to derive
the first-order field equations on the middle brane. The effective theory is a
generalized Brans-Dicke theory with two scalar fields. This is conformally
equivalent to Einstein gravity and two scalar fields, minimally coupled to the
geometry, but nonminimally coupled to matter on the three branes.
