  Stability and localization of the gravitational perturbations for a special
brane system in Eddington-inspired Born-Infeld (EiBI) gravity were studied in
[Phys. Rev. D 85, 124053 (2012)]. In this paper, we show that the gravitational
perturbations for a general brane system are stable, the four-dimensional
graviton (massless KK graviton) can be localized on the brane, and the mass
spectrum of massive KK gravitons are gapless and continuous. Two models are
constructed as examples. In the first model, which is a generalization of
[Phys. Rev. D 85, 124053 (2012)], the brane has no inner structure and there is
no gravitational resonance (quasi-localized KK gravitons). In the second one,
the background scalar field is a double-kink when the parameter in the model
approaches its critical value. Correspondingly, the brane has inner structure
and some gravitational resonances appear.
