Ternary alloys of platinum group metals attract a growing interest due to their unique catalytic properties. The present research is aimed to synthesize a series of Rh-Pd-Pt alloys with varied ratios of metals using a single-source precursor approach. Rhodium and palladium are partly miscible metals, while each of these metals is unlimitedly miscible with platinum. Thermolysis of complex salts used as a precursor results in the formation of metastable systems. The 3D nanostructure alloys are being formed after the complete decomposition of the single-source precursor. High-resolution transmission electron microscopic studies have shown that the nanoalloys are composed of interconnected polycrystalline ligaments with a mean diameter of 50 nm. The single-phase composition is confirmed by an X-ray diffraction analysis. The ratio of metals plays an important role in determining the catalytic activity of alumina-supported alloys and their thermal stability. According to UV-vis spectroscopy data, the higher palladium portion corresponds to worse dispersion of initially prepared, fresh catalysts. Treatment of the catalysts under prompt thermal aging conditions (up to 800 °C) causes redispersion of palladium-rich alloyed nanoparticles, thus leading to improved catalytic activity and thermal stability.