We demonstrate a mechanism for realizing ferrimagnetic metal, antiferromagnetic half-metal, and paramagnetic metal phases by tuning the onsite Coulomb repulsion U in a band insulator. In a simple model of a correlated band insulator, namely the ionic Hubbard model at half-filling, and in the presence of a second neighbor hopping, we show that as U is increased, first he insulating band gap is suppressed to zero at a critical U-1 and remains zero within the paramagnetic metallic phase. Interestingly, at a larger U-c, ferrimagnetic order turns on, leading to a ferrimagnetic metallic phase for U-c < U < U-2. For U > U-2, the system exhibits an antiferromagnetic half-metallic phase, followed finally by a transition into an antiferromagnetic Mott insulator. Our results, based on dynamical mean-field theory, suggest alternate routes for achieving magnetically ordered metallic and half-metallic phases which have potential applications in spintronics.