  Braneworld models with induced gravity have the potential to replace dark
energy as the explanation for the current accelerating expansion of the
Universe. The original model of Dvali, Gabadadze and Porrati (DGP) demonstrated
the existence of a ``self--accelerating'' branch of background solutions, but
suffered from the presence of ghosts. We present a new large class of
braneworld models which generalize the DGP model. Our models have negative
curvature in the bulk, allow a second brane, and have general brane tensions
and localized curvature terms. We exhibit three different kinds of ghosts,
associated to the graviton zero mode, the radion, and the longitudinal
components of massive graviton modes. The latter two species occur in the DGP
model, for negative and positive brane tension respectively. In our models, we
find that the two kinds of DGP ghosts are tightly correlated with each other,
but are not always linked to the feature of self--acceleration. Our models are
a promising laboratory for understanding the origins and physical meaning of
braneworld ghosts, and perhaps for eliminating them altogether.
