We present a systematic study of electrical resistivity, superconductive transitions and the Hall effect for three systems of compositionally complex amorphous alloys of early (TE) and late (TL) transition metals: (TiZrNbNi)1−xCux and (TiZrNbCu)1−xCox in a broad composition range of 0<x<0.5 as well as Ti0.30Zr0.15Nb0.15Cu0.2Ni0.2, Ti0.15Zr0.30Nb0.15Cu0.2Ni0.2 and Ti0.15Zr0.15Nb0.30Cu0.2Ni0.2. All samples showed high resistivity at room temperature, 140–240 μΩ cm, and the superconducting transition temperatures decreased with increasing late transition metal content, similar to binary amorphous and crystalline high-entropy TE-TL alloys. The Hall coefficient RH was temperature-independent and positive for all samples (except for (TiZrNbCu)0.57Co0.43), in good agreement with binary TE-TL alloys. Finally, for the temperature dependence of resistivity, as far as the authors are aware, we present a new model with two conduction channels, one of them being variable range hopping, such as the parallel conduction mode in the temperature range 20–200 K, with the exponent p=1/2. We examine this in the context of variable range hopping in granular metals.