The formation of quaternary rare-earth (RE) germanides containing transition metals (M's) from groups 6 to 10 was investigated through arc-melting and annealing reactions at 800 °C; about 50 new compounds were obtained. These include several new series of quaternary germanides RE4M2InGe4 (M = Fe, Co, Ru, Rh, Ir), previously known only for M = Mn and Ni; additional members of RE4Ni2InGe4 extended to other RE substituents; and a different but closely related series RE4RhInGe4. Detailed crystal structures were determined by single-crystal X-ray diffraction studies for 20 compounds. Monoclinic structures in space group C2/m are adopted by RE4M2InGe4 (Ho4Ni2InGe4-type, a = 15.1-16.5 Å, b = 4.1-4.4 Å, c = 6.9-7.3 Å, β = 106.2-108.6°) and RE4RhInGe4 (own type, a = 20.0-20.2 Å, b = 4.2-4.3 Å, c = 10.1-10.2 Å, β = 105.0-105.3°). Both structures contain frameworks built from MGe4 tetrahedra, InGe4 square planes, and Ge2 dimers, delimiting tunnels occupied by RE atoms. These structures can also be derived by cutting slabs along different directions from the more symmetrical RE2InGe2 structure. Although the Ge2 dimers are relatively invariant, the InGe4 square planes can undergo distortion to form two sets of short versus long In-Ge distances. This distortion results from a competition between M-Ge bonding in the MGe4 tetrahedra and In-Ge bonding in the InGe4 square planes.