Motivated by the first search for the rare charged-current B decay to four leptons, $$\ell \bar{\nu }_\ell \ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ $\ell {\overline{\nu }}_{\ell }{\ell }^{(\prime )}{\overline{\ell }}^{(\prime )}$ , we calculate the decay amplitude with factorization methods. We obtain the $$B\rightarrow \gamma ^*$$ $B\to {\gamma }^{\ast }$ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $$\Lambda _\mathrm{QCD}/m_b$$ ${\Lambda }_{\mathrm{QCD}}/m_b$ to next-to-leading order in $$\alpha _s$$ ${\alpha }_s$ , and at $$\mathcal {O}(\alpha _s^0)$$ $O\left({\alpha }_s^0\right)$ at next-to-leading power. Our calculations predict branching fractions of a few times $$10^{-8}$$ ${10}^{-8}$ in the $$\ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ ${\ell }^{(\prime )}{\overline{\ell }}^{(\prime )}$ mass-squared bin up to $$q^2=1~$$ $q^2=1$ GeV $$^2$$ ${}^2$ with $$n_+q>3~$$ $n_{+}q>3$ GeV. The branching fraction rapidly drops with increasing $$q^2$$ $q^2$ . An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment $$\lambda _B$$ ${\lambda }_B$ of the leading-twist B meson light-cone distribution amplitude. We find that in the small- $$q^2$$ $q^2$ bin, the sensitivity to $$\lambda _B$$ ${\lambda }_B$ is almost comparable to $$B^- \rightarrow \mathrm {\ell }^- \bar{\nu }_{\mathrm {\ell }}\gamma $$ $B^{-}\to {\ell }^{-}{\overline{\nu }}_{\ell }\gamma$ when $$\lambda _B$$ ${\lambda }_B$ is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger $$q^2$$ $q^2$ .