Extensions of the standard electroweak ${G}^{0}\ensuremath{\equiv}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ gauge model, which include more neutral vector bosons, are strongly restricted but not excluded by the Hung-Sakurai (HS) factorization relations on neutrino-quark, neutrino-electron, and electron-quark amplitudes. As might be naively expected, the HS relations are satisfied for any gauge group ${\mathcal{G}}_{0}\ensuremath{\equiv}{G}^{0}\ifmmode\times\else\texttimes\fi{}{G}^{\ensuremath{'}}$ provided that all the mentioned fermions transform as singlets under ${G}^{\ensuremath{'}}$. The only nontrivial extensions which preserve the HS relations are shown to be left-right-symmetric models based on the group $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{V}$ and its subgroup $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{{I}_{3}R}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{V}$, independent of the manner in which the spontaneous symmetry breaking occurs.