  A 510 day long-term measurement of a 45.3 g platinum foil acting as the
sample and high voltage contact in an ultra-low-background high purity
germanium detector was performed at Laboratori Nazionali del Gran Sasso
(Italy). The data was used for a detailed study of double beta decay modes in
natural platinum isotopes. Limits are set in the range $\mathcal{O}(10^{14} -
10^{19})$ yr (90% C.L.) for several double beta decay transitions to excited
states confirming, and partially extending existing limits. The highest
sensitivity of the measurement, greater than $10^{19}$ yr, was achieved for the
two neutrino and neutrinoless double beta decay modes of the isotope
$^{198}$Pt. Additionally, novel limits for inelastic dark matter scattering on
$^{195}$Pt are placed up to mass splittings of approximately 500 keV. We
analyze several techniques to extend the sensitivity and propose a few
approaches for future medium-scale experiments with platinum-group elements.
