  We explore models of intersecting brane-worlds with induced gravity terms on
codimension one branes and on their intersection. Maximally symmetric solutions
for the branes and the intersection are found. We find new self-accelerating
solutions. In a 6d spacetime, the solutions realize the see-saw modification of
gravity where the UV scale of the modification to 4d gravity is determined by
6d Planck scale given by $M_6 \sim 10^{-3}$eV and the IR scale of the
modification is determined by $M_6^2/M_4 \sim H_0 \sim 10^{-42}$ GeV where
$H_0$ is present-day Hubble scale. We find that it is increasingly difficult to
construct phenomenologically viable models in higher-dimensional spacetime due
to the necessity to have the lower value for the fundamental Planck scale to
realize the late time acceleration. It is found that the system also admits
self-tuning solutions where the tension at the intersection does not change the
geometry of the intersection. The induced gravity terms can avoid the necessity
to compactify the extra dimensions. Finally, we discuss the possibility to have
ordinary matter at the intersection, without introducing any regularisation,
using the induced gravity terms.
