The alloys RNi2Mn and RCo2Mn with R representing the rare earth element are isostructural analogues of the binary Laves phases RNi2, RCo2. We have synthesized the isoelectronic Pd-based RPd2Mn analogues with R = Gd, Tb, and Dy, for the first time. They crystallize in a cubic structure, however, not in the cubic C15 (Fd-3m) structure of RNi2Mn, nor the Laves phase' structure. Instead, the crystal lattice is described by the Im-3m space group with Tb/Dy, Pd, and Mn atoms randomly distributed over the 2a Wyckoff position of the W-type structure (A2, disordered bcc). The magnetization data reveal a standard paramagnetic behavior, with effective magnetic moments strikingly close to those expected for Tb 3+ and Dy 3+ free ions, down to 130 K.