  We show that dark matter with a per-nucleon scattering cross section $\gtrsim
10^{-28}~{\rm cm^2}$ could be discovered by liquid scintillator neutrino
detectors like BOREXINO, SNO+, and JUNO. Due to the large dark matter fluxes
admitted, these detectors could find dark matter with masses up to $10^{21}$
GeV, surpassing the mass sensitivity of current direct detection experiments
(such as XENON1T and PICO) by over two orders of magnitude. We derive the
spin-independent and spin-dependent cross section sensitivity of these
detectors using existing selection triggers, and propose an improved trigger
program that enhances this sensitivity by two orders of magnitude. We interpret
these sensitivities in terms of three dark matter scenarios: (1) effective
contact operators for scattering, (2) QCD-charged dark matter, and (3) a
recently proposed model of Planck-mass baryon-charged dark matter. We calculate
the flux attenuation of dark matter at these detectors due to the earth
overburden, taking into account the earth's density profile and elemental
composition, and nuclear spins.
