  We present the Galactic Radio Explorer (GReX), an all-sky monitor to probe
the brightest bursts in the radio sky. Building on the success of STARE2, we
will search for fast radio bursts (FRBs) emitted from Galactic magnetars as
well as bursts from nearby galaxies. GReX will search down to ~ten microseconds
time resolution, allowing us to find new super giant radio pulses from Milky
Way pulsars and study their broadband emission. The proposed instrument will
employ ultra-wide band (0.7--2 GHz) feeds coupled to a high performance
(receiver temperature <10 K) low noise amplifier (LNA) originally developed for
the DSA-110 and DSA-2000 projects. In GReX Phase I (GReX-I), unit systems will
be deployed at Owens Valley Radio Observatory (OVRO), NASA's Goldstone station,
and at Telescope Array, Delta Utah. Phase II will expand the array, placing
feeds in India, Australia, and elsewhere in order to build up to continuous
coverage of nearly 4$\pi$ steradians and to increase our exposure to the
Galactic plane. We model the local magnetar population to forecast for GReX,
finding the improved sensitivity and increased exposure to the Galactic plane
could lead to dozens of FRB-like bursts per year.
