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Hydrogen-rich superhydrides are believed to be very promising high critical temperature (high T_{c}) superconductors, with experimentally observed critical temperatures near room temperature, as shown in recently discovered lanthanide superhydrides at very high pressures, e.g., LaH_{10} at 170 GPa and CeH_{9} at 150 GPa. With the motivation of discovering new hydrogen-rich high T_{c} superconductors at the lowest possible pressure, quantitative theoretical predictions are needed. In these promising compounds, superconductivity is mediated by the highly energetic lattice vibrations associated with hydrogen and their interplay with the electronic structure, requiring fine descriptions of the electronic properties, notoriously challenging for correlated f systems. In this paper, we propose a first-principles calculation platform with the inclusion of many-body corrections to evaluate the detailed physical properties of the Ce-H system and to understand the structure, stability, and superconductivity of CeH_{9} at high pressure. We report how the calculation of T_{c} is affected by the hierarchy of many-body corrections and obtain a compelling increase in T_{c} at the highest level of theory, which goes in the direction of experimental observations. Our findings shed significant light on the search for superhydrides in close similarity with atomic hydrogen within a feasible pressure range. We provide a practical platform to further investigate and understand conventional superconductivity in hydrogen-rich superhydrides.