Multireference CI calculations predict fourteen states of BN2+ to be quasibound, an uncommonly large number for a first-row diatomic, confirming the important role played by the electropositive B atom in stabilizing molecular dications. About two-thirds of the metastable potentials have dissociation barriers (D-eff) between 0.59 and 2.25 eV, accommodating several vibrational levels and therefore being kinetically stable. The ground state X (3) Sigma(-), however, might be difficult to study experimentally because it is only weakly bound (D-eff=0.23 eV), and its formation via ionization of BN or BN+ has unfavorable Franck-Condon factors (FCF). The 1 (5) Sigma(-) state is the best candidate for detecting BN2+ : Its barrier is the highest (D-eff-2.25 eV), sustaining about 30 vibrational levels (with tunneling lifetimes tau(upsilon)(T) approximate to infinity for upsilon < 20), and the ionization FCFs are favorable. The 1 (1) Delta state might also be detectable since its properties are similar to those of 1 (5) Sigma(-). Near equilibrium, most metastable states are described by the configurations 3 sigma(2)4 sigma 5 sigma 1 pi(2) and 3 sigma(2)4 sigma 1 pi(3), both having charge distributions B2+N. The adiabatic ionization potential into BN2+ (X (3) Sigma(-)) is 21.4 eV for ionization from BN+ (X (4) Sigma(-)) and 32.9 eV from BN(X (3) Pi). The corresponding IPs into 1 (5) Sigma(-) lie 1.12 eV higher.