Towards King - plot nonlinearity measurements in Pd and Pd⁺

King plots are the graphical representations of the linear relationships of the isotope shift of two transitions of the same element. Deviations of linearity in these plots may be sensitive to beyond the standard model (BSM) interactions of some new light boson to neutrons. As hyperfine structure and second order field shifts serve as sources of non BSM King plot nonlinearities, an ideal element to use in a King plot nonlinearity search is one with (1) a long chain of spin-zero isotopes, (2) measureable narrow transitions, and (3) small nuclear deformation.  Palladium (Z= 46) is one such element with its five stable spin-zero isotopes. We describe our plans to carry out isotope shift measurements in Pd and Pd⁺ towards performing a King Plot nonlinearity test.