  For many years annually modulating $\sim$ keV scintillations have been
observed in the DAMA/NaI and DAMA/Libra experiments. A dark matter - electron
scattering interpretation is now favoured given the stringent constraints on
nuclear recoil rates obtained by LUX, SuperCDMS and other experiments. Very
recently, the XENON100 experiment has observed a modest annual modulation in
their electron recoil events (2.8 $\sigma$ C.L.) with phase consistent with
that of the DAMA experiments. However, they also found a stringent upper limit
on the unmodulated rate, which suggests that any dark matter - electron
scattering interpretation of these annual modulations must involve a large
modulation fraction $\stackrel{>}{\sim} 50\%$. Here we discuss the extent to
which these results might be able to be accommodated within multi-component
dark matter models featuring light dark matter particles of mass $\sim$ MeV,
focusing on the mirror dark matter case for definiteness. The importance of
diurnal variation as a means of testing these kinds of models is also
discussed.
