We consider a Hubbard model in the square lattice, with a generalized hopping between nearest-neighbor sites for spin up (down), which depends on the total occupation n b of spin down (up) electrons on both sites. We call the hopping parameters t AA , t AB , and t BB for n b = 0, 1 or 2 respectively. Using the Hartree-Fock and Bardeen-Cooper-Schrieffer mean-field approximations to decouple the two-body and three-body interactions, we find that the model exhibits extended s-wave superconductivity in the electron-hole symmetric case t AB > t AA = t BB for small values of the Coulomb repulsion U or small band fillings. For moderate values of U, the antiferromagnetic normal (AFN) state has lower energy. The translationally invariant d-wave superconducting state has always larger energy than the AFN state.