We use a thermodynamic framework for silicate-metal partitioning to determine the possible compositions of metallic cores on super-Earths. We compare results using literature values of the partition coefficients of Si and Ni, as well as new partition coefficients calculated using results from laser shock-induced melting of powdered metal-dunite targets at pressures up to 276 GPa, which approaches those found within the deep mantles of super-Earths. We find that larger planets may have little to no light elements in their cores because the Si partition coefficient decreases at high pressures. The planet mass at which this occurs will depend on the metal-silicate equilibration depth. We also extrapolate the equations of state (EOS) of FeO and FeSi alloys to high pressures, and present mass-radius diagrams using self-consistent planet compositions assuming equilibrated mantles and cores. We confirm the results of previous studies that the distribution of elements between mantle and core will not be detectable from mass and radius measurements alone. While observations may be insensitive to interior structure, further modeling is sensitive to compositionally dependent properties, such as mantle viscosity and core freeze-out properties. We therefore emphasize the need for additional high pressure measurements of partitioning as well as EOSs, and highlight the utility of the Sandia Z-facilities for this type of work.