The electron-induced ${L}_{3}M$ two-step double ionization cross sections of metallic Pd were determined experimentally for incident electron beam energies ranging from the double ionization threshold up to 18 keV. The double ${L}_{3}M$ ionization cross sections were derived from the intensity ratios (${I}_{L\ensuremath{\alpha}M}$:${I}_{L\ensuremath{\alpha}}$) of the resolved $M$ satellites to the parent diagram lines. The sample was bombarded with monoenergetic electrons from an energy-tunable 20-kV electron gun. The diagram and $M$-satellite x-ray lines were measured by means of high-resolution x-ray spectroscopy, using a reflection-type von Hamos bent crystal spectrometer. The two-step partial cross sections were determined by subtracting from the measured total double ionization cross sections the contributions due to the shake process and ${L}_{1}$-${L}_{3}{M}_{4,5}$ Coster-Kronig transitions. Despite the thick target employed in the present study, the dependence of the two-step cross sections on the incoming electron energy could be derived using a target slice decomposition method. It is shown that the obtained energy dependence can be well reproduced by the semiempirical parametrization model of Pattard and Rost.