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 muliplicity 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 , a rate of 70 \pm 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 . Based on these studies , we also discuss the benefits of using a neutron multiplicity meter as a component of active shielding in such experiments .