Local spin density calculations for the large enhanced paramagnet ZrV₂ in the C15 structure have been performed. The ground-state is paramagnetic but almost degenerate with the ferromagnetic state. Here we study diferent ways to trigger ferromagnetism. First we study the possibiliiy of having thermal excitations between non-magnetic and magnetic states, in which case a anti invar effect would be possible. Secondly, in calculations with V core holes which are models of X-ray absorption spectroscopy (XAS) we study the possibility of having induced magnetism via core polarization. Calculations of complete XAS spectra including matrix elements suggest that these nearly magnetic systems are good candidates for giving quite unusual results in spectroscopy measurements.