Can dark matter - electron scattering explain the DAMA annual modulation consistent with XENON100 constraints?

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.