We investigate stationary models of magnetized, self-gravitating disks around black holes. The disks are assumed to rotate according to a recently introduced Keplerian rotation law. We consider different prescriptions of the toroidal magnetic field. Similarly to the purely hydrodynamical case (i.e., with no magnetic field), we observe a bifurcation in the parameter space of solutions. There are usually two branches of solutions: a branch corresponding to relatively light disks and a branch for which the disk can be more massive than the black hole. The existence of this latter branch can be explained by geometric properties of the spacetime. We investigate the influence of the magnetic field in the disk on these effects.