Ab initio molecular dynamics simulations are used to systematically explore the influence of alloying on the stiffness and plasticity of Co-Fe-Ta-B metallic glasses. The Co43.5Ta6.1B50.4 metallic glass studied in this work, with a Young's modulus of 295 GPa, is the stiffest metallic glass known in literature. From the analysis of the density of the states it is suggested that the very large stiffness is due to strong covalent metal to boron bonding. Furthermore it has been observed that by alloying with Y, Zr, Nb, Mo, Hf, W, C, N and O the bulk to shear modulus ratio can be varied from 2.08 to 2.82. As noted by Lewandowski et al (2005 Phil. Mag. Lett. 85 77) a brittle to plastic transition for metallic glasses can be identified in the range of 2.33 to 2.44. Hence, it is evident that the whole range from brittle to plastic behaviour can be covered, with the systems studied in this work. This evolution from brittle to plastic behaviour can be attributed to a change from predominately covalent to predominately metallic bond character.