  Laves-phase Nb{1+c}Fe_{2-c} is a rare itinerant intermetallic compound
exhibiting magnetic quantum criticality at c_{cr}=1.5%Nb excess; its origin,
and how alloying mediates it, remains an enigma. For NbFe_2, we show that an
unconventional band critical point (uBCP) above the Fermi level E_F explains
most observations, and that chemical alloying mediates access to this uBCP by
an increase in E_F with decreasing electrons (increasing %Nb), counter to
rigid-band concepts. We calculate that E_F enters the uBCP region for c_{cr} >
1.5%Nb and by 1.74%Nb there is no Nb site-occupation preference between
symmetry-distinct Fe sites, i.e., no electron-hopping disorder, making
resistivity near constant as observed. At larger Nb (Fe) excess, the
ferromagnetic Stoner criterion is satisfied.
