Hydrides of period 2 and 3 elements are promising candidates for hydrogen storage but typically have heats of reaction that are too high to be of use for fuel cell vehicles. Recent experimental work has focused on destabilizing metal hydrides through alloying with other elements. A very large number of possible destabilized metal hydride reaction schemes exist. The thermodynamic data required to assess the enthalpies of these reactions, however, are not available in many cases. We have used first principles density functional theory calculations to predict the reaction enthalpies for more than 100 destabilization reactions that have not previously been reported. Many of these reactions are predicted not be useful for reversible hydrogen storage, having calculated reaction enthalpies that are either too high or too low. More importantly, our calculations identify five promising reaction schemes that merit experimental study: 3LiNH(2) -> 2LiH + Si -> Li5N3Si + 4H(2), 4LiBH(4) + MgH2 -> 4LiH + MgB4 + 7H(2), 7LiBH(4) + MgH2 -> 7LiH + MgB7 + 11.5H(2), CaH2 + 6LiBH(4) -> CaB6 + 6LiH + 10H(2), and LiNH2 + MgH2 -> LiMgN + 2H(2).