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 DGPinspired F(R, φ) 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, φ) scenario has the best fit with LCDM and recent observations than other alternative theories.
