The Large Volume Detector (LVD) in the Gran Sasso Laboratory of INFN is a modular detector mainly devoted to search for neutrinos from core collapse super-novae. It is made of 1000 tons of liquid scintillator divided in 840 stainless steel tanks 1.5m3 each. We present the possibility for LVD to work both as a passive shield and moderator for the gamma and neutron background and as an active veto to reduce the higher energy background coming from muon induced neutrons. An inner region inside the LVD structure (‘LVD Core Facility’) can be identified, with a volume of about 30m3, with the neutron background typical of an underground laboratory placed at a much deeper site. This region can be realized with a negligible impact on the LVD operation and its sensitive mass. The LVD Core Facility could be effectively exploited by a compact experiment for the search of rare events, such as double beta decay or dark matter. A possible candidate could be a liquid Xenon double phase detector.
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