  Based on the Lue-Starkman conjecture on the dynamical screening of the brane
cosmological constant in the DGP scenario, we extend this proposal to a general
DGP-inspired $F(R,\phi)$ Model. We show that modification of the induced
gravity and its coupling to a quintessence field localized on the brane,
affects the screening of the brane cosmological constant and also phantom-like
behavior on the brane. We extend our study to possible modification of the
induced gravity on the brane and for clarification some specific examples are
presented. As a result, phantom-like behavior can be realized in this setup
without violating the null energy condition at least in some subspaces of the
model parameter space. The key result of our study is the fact that a
DGP-inspired $F(R,\phi)$ scenario has the best fit with LCDM and recent
observations than other alternative theories.
