The feasibility of producing the molecular antihydrogen anion ${{\overline{\mathrm{H}}}_{2}}^{\ensuremath{-}}$ in the laboratory is investigated. Utilizing reaction rates calculated here involving the interaction of laser excited-state antihydrogen atoms held in magnetic minimum traps, key processes are identified that could lead to anion production, as well as competing effects leading to anti-atom loss. These are discussed in the context of present-day and near-future experimental capabilities.