  The current paradigm for dark matter direct detection is to assume that the
dark sector is solely composed of a single particle species. In this short
paper, we make the observation that dark matter comprising both a light and a
heavy component that modulate out of phase leads to interesting phenomenology
in annual modulation experiments. For an illustrative example, we use the
recently released DAMA/LIBRA phase-2 results with a lower energy threshold.
Immediately after, it was argued that a one-component spin-independent dark
matter explanation of the observed annual modulation is strongly disfavored or
excluded unless isospin-violating couplings are invoked. We show that a simple
two-component extension can reproduce the observed spectrum without the need to
invoke fine-tuned couplings. Using the publicly available DAMA/LIBRA data, we
perform a fit of the DAMA/LIBRA energy spectrum of the annual modulation
amplitude to a scenario with two dark matter components. We also take into
account how gravitational focusing affects the phases of the light and a heavy
components differently, which leads to nontrivial effects in the total
time-dependent rate. Our results show that there exists a unique solution in
agreement with the data in the simplest case of isospin-conserving couplings
with equal cross sections. The distinctive features found in this work are
crucial for a dark matter interpretation of any observed annual modulation.
