A study of the Fermi surface of the putative topological semimetal Pd$_3$Pb has been carried out using Shubnikov-de Haas (SdH) oscillations measured in fields of up to 60 T. Pd$_3$Pb has garnered attention in the community due to a peculiar Fermi surface that has been proposed theoretically by Ahn, Pickett, and Lee, [Phys. Rev. B 98, 035130 (2018)] to host a dispersion-less band along $X-Gamma$ as well as multiple triply-degenerate band crossings that, under the influence of spin-orbit coupling, lead to ten four-fold degenerate Dirac points. Analysis of the SdH oscillation data verifies the calculated multi-sheet Fermi surface, revealing a $Gamma$ centered spheroid that had not been resolved experimentally in prior studies. A comprehensive, angle-dependent analysis of the phase of the SdH oscillations convincingly demonstrates a non-trivial Berry phase for two bands along $Gamma-R$, supporting the theoretical predictions, while simultaneously evidencing interference between extremal orbits that mimics a trivial Berry phase at intermediate angles.
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