It has been shown recently that phantom-like effect can be realized on the normal branch of the DGP setup without introduction of any phantom matter in the bulk or on the brane and therefore without violation of the null energy condition. Inclusion of the Gauss–Bonnet term in the bulk action modifies this picture via curvature effects. 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, ) model that stringy effects in the ultraviolet sector of the theory are taken into account by inclusion of the Gauss–Bonnet term in the bulk action. We study cosmological dynamics of this setup, especially its phantom-like behavior and possible crossing of the phantom divide line. In this setup, scalar field and curvature quintessence are treated in a unified framework.