Working in the framework of the ab-initio no-core shell model, we derive two-body effective interactions microscopically for specific harmonic-oscillator basis spaces from the realistic Argonne V8' nucleon-nucleon potential. However, our two-body effective interaction is only the dominant part of the A-body (A >= 3) effective interaction, which also contains three-, four- and, in general, up to A-body components. We model these multi-body components as a simple two-parameter, basis-space-dependent interaction. We then investigate the coupling needed to provide accurate descriptions of selected nuclear observables. We successfully model the multi-body interaction as a zero-range two-body operator times the number operator Nsps that measures the harmonic-oscillator quanta of the spectator nucleons.