We suggest that a singlet fermion S exists beyond the standard see-saw structure. It mixes with light neutrinos via interactions with the right-handed neutrino components, so that nu e --> S conversion solves the solar neutrino problem. Supersymmetry endowed with R-symmetry is shown to give a natural framework for existence, mass scale (similar to 3 . 10(-3) eV) and mixing (sin(2) 2 theta(es) similar to (0.1-1.5) . 10(-2)) of such a fermion. Models with an approximate horizontal symmetry are constructed, which embed the fermion S and explain simultaneously solar, atmospheric, hot dark matter problems as well as may predict the oscillation <(nu)over bar>(mu) --> <(nu)over bar>(e) in the region of sensitivity of KARMEN and LSND experiments.