  We estimate the maximum direct detection cross section for sub-GeV dark
matter (DM) scattering off nucleons. For DM masses in the range $10 \text{ keV
}- 100 \text{ MeV}$, cross sections greater than $10^{-36}$- $10^{-30}
\,\text{cm}^2$ seem implausible. We present a DM candidate which realizes this
maximum cross section: HighlY interactive ParticlE Relics (HYPERs). After
HYPERs freeze-in, a dark sector phase transition decreases the mediator's mass.
This increases the HYPER's direct detection cross section without impacting its
abundance or measurements of Big Bang Nucleosynthesis and the Cosmic Microwave
Background.
