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Recently, superhydrides have been computationally identified and subsequently synthesized with a variety of metals at very high pressures. In this work, we evaluate the possibility of synthesizing superhydrides by uniquely combining electrochemistry and applied pressure. We perform computational searches for palladium superhydrides using density functional theory and particle swarm optimization calculations over a broad range of pressures and electrode potentials. We incorporate exchange-correlation functional uncertainty using the Bayesian error estimation formalism to quantify the uncertainty associated with the identified stable phases. Based on a thermodynamic analysis, we construct pressure-potential phase diagrams and provide an alternate synthesis concept, $\mathcal{P}^2$ (pressure-potential), to accessing novel phases having high hydrogen content. Palladium-hydrogen is a widely-studied material system with the highest hydride phase being Pd$_3$H$_4$. Most strikingly for this system, at potentials above hydrogen evolution and $\sim$300 MPa pressure, we find the possibility to make palladium superhydrides (e.g., PdH$_{10}$). We demonstrate the generalizability of this approach for La-H, Y-H and Mg-H with 10-100 fold reduction in required pressure for stabilizing phases. In addition, the $\mathcal{P}^2$ strategy allows stabilizing new phases that cannot be done purely by either pressure or potential and is a general approach that is likely to work for synthesizing other superhydrides at modest pressures.