A search for double beta decays of ¹¹⁰Pd and ¹⁰²Pd into excited states of the daughter nuclides has been performed using three ultra-low background gamma-spectrometry measurements in the Felsenkeller laboratory, Germany, the HADES laboratory, Belgium and at the LNGS, Italy. The combined Bayesian analysis of the three measurements sets improved half-life limits for the 2vββ and 0vββ decay modes of the 21⁺, 01⁺ and 2⁺2 transitions in 110Pd to 2.9 - 10²⁰ yr, 4.0 - 1020 yr and 3.0 - 10²⁰ yr, respectively, and in 102Pd to 7.6 - 10¹⁸ yr, 8.8 - 10¹⁸ yr and 1.4 - 10¹⁹ yr, respectively, with 90% credibility.