  We explore extensions of inelastic Dark Matter and Magnetic inelastic Dark
Matter where the WIMP can scatter to a tower of heavier states. We assume a
WIMP mass $m_\chi \sim \mathcal{O}(1-100)$ GeV and a constant splitting between
successive states $\delta \sim\mathcal{O}(1 - 100)$ keV. For the
spin-independent scattering scenario we find that the direct experiments CDMS
and XENON strongly constrain most of the DAMA/LIBRA preferred parameter space,
while for WIMPs that interact with nuclei via their magnetic moment a region of
parameter space corresponding to $m_{\chi}\sim 11 $ GeV and $\delta < 15$ keV
is allowed by all the present direct detection constraints.
