Based on the earlier revealed hidden pseudo Jahn-Teller effect which essentially involves excited electronic states we show that, with extension to solids, polyatomic systems with half-filled degenerate shells, e(2) or t(3), form a novel (practically inexhaustible) class of molecular and solid state materials with correlated and switchable magnetic and dielectric bistabilities. The latter are confirmed by state-of-the-art ab initio calculations, including estimation of lifetimes, for several representatives of this class, which also reveal a giant magnetoelastic effect in LiCuO(2) and NaCuO(2) crystals.