  Thermal freeze-out or freeze-in during a period of early matter domination
can give rise to the correct dark matter abundance for $\langle \sigma_{\rm
ann} v \rangle_{\rm f} < 3 \times 10^{-26}$ cm$^3$ s$^{-1}$. In the standard
scenario, a single field that behaves like matter drives the early matter
dominated era. However, in realistic models, this epoch may involve more than
one field. In this paper, we study the effect of such a modification on the
production of dark matter during early matter domination. We show that even a
subdominant second field that decays much faster than the dominant one can
considerably enhance the temperature of the universe during an early
matter-dominated phase. This in turn affects dark matter production via
freeze-out/in and opens up the allowed parameter space toward significantly
larger dark matter masses. As a result, one can comfortably obtain the correct
relic abundance for PeV-scale dark matter for reheating temperatures at or
below 10 GeV.
