We present, for the first time, the design of an instrument capable of measuring the high energy ( > 60 MeV ) muon-induced neutron flux deep underground. The instrument is based on applying the Gd-loaded liquid-scintillator technique to measure the rate of multiple low-energy neutron events produced in a Pb target and from this measurement to infer the rate of high energy neutron events. This unique signature allows both for efficient tagging of neutron multiplicity events as well as rejection of random gamma backgrounds so effectively that typical low-background techniques are not required. We present design studies based on Monte Carlo simulations that show that an apparatus consisting of a Pb target of 200 cm by 200 cm area by 60 cm thickness covered by a 60 cm thick Gd-loaded liquid scintillator (0.5% Gd content) detector could measure, at a depth of 2000 meters of water equivalent (m.w.e), a rate of 70 ± 8 (stat) events/year with a background of less than 10 events/year. We discuss the relevance of this technique to measuring the muon-induced neutron background in searches for dark matter in the form of Weakly Interacting Massive Particles (WIMP). Based on these studies, we also discuss the benefits of using a neutron multiplicity meter as a component of active shielding in such experiments.