The viscoelastic behavior of four different bulk metallic glass (BMG) systems, i.e., Cu46Zr46Al8, Cu44Zr44Al8Co4, Cu44Zr44Al8Hf4, and Cu44Zr44Al8Co2Hf2, is investigated concerning its deformation-mode dependence via dynamic mechanical analysis (DMA) in 3-point bending (TPB), tension, and torsion modes. At temperatures below the glass transition, the considered BMGs deform primarily elastic, and the mechanical response is independent of the testing frequency, whereas, in the glass transition region, the viscoelastic component dominates. Crystallization decreases the viscoelastic contribution, whereas plastic deformation leads to an increase in atomic mobility for all three deformation modes. Compared to tension and torsion, TPB is found to be more sensitive to dynamic mechanical stress. TPB generates a complex stress state in the matrix and can thus introduce substantial variations in loss modulus. Structural analyses carried out by transmission electron microscopy and X-ray diffraction confirmed the amorphous nature of the base composition and structural changes when heated to the intermediate peak temperature observed at 743 K for the TPB mode. Compared to Cu46Zr46Al8, 4 at. pct Co addition in the Cu46−x\2Zr46−x\2Al8Cox amorphous alloy leads to a glass showing relatively higher thermomechanical stability around its glass transition. This study provides evidence for the enhancement of the mechanical properties of CuZr-based BMGs at elevated temperatures by microalloying.