There is an increasing awareness of the need for development of effective nuclear security systems in the context of security related to major public events such systems include detection of radiation levels that may originate from intentionally placed nuclear - or other radioactive - material by criminal or unauthorised actors. According to the IAEA-NSS 18 - Nuclear Security Systems and Measures for Major Public Events /Implementing Guide - procedures for background radiation mapping and screening of venues for the detection of nuclear or other radioactive materials outside of regulatory control (MORC) before the major public event are required measures. We present preliminary results of a conceptual design study for an organic-scintillator-based mobile radiation screening system with improved features that, additionally, enables a signature detection of special nuclear material (SNM). Organic scintillators have a high sensitivity to fast neutrons and gamma-rays. Such radiation detector materials with the additional ability to discriminate between the two particle types by means of pulse shape discrimination (PSD) are commercially available in the form of solid plastic scintillators, single-crystal organic scintillators like Stilbene, or liquid scintillators. Detection systems based on such materials are excellent for general-purpose radiation detection with limited radionuclide identification capabilities. In addition, they enable detection of fast gamma-neutron and neutron-neutron coincidences, which is an effective way to determine a clean signature of SNM, since these particles are correlated in time when emitted during the fission process. The modelling of a mobile scanning system in different configurations and conditions is carried out using the Monte Carlo codes, MCNP6.2 and GEANT4. Preliminary results show high sensitivity, so that the system when mounted on an unmanned aerial or ground-based vehicle together with an integrated Global Position System (GPS) information promises an advanced radiological mapping in an unattended way. The possibility of adding high- or medium-resolution radionuclide identification detectors to the system is also discussed.