The widely recognized MAX-phase materials consist of an early transition metal (M), an A-group element, and carbon or nitrogen (X) in a hexagonal layered crystal structure. Recently, materials known as MAB phase materials have been developed by substituting boron (B) for the carbon or nitrogen. We have studied an MAB phase alloy system, Hf2(S,Te)B${\rm Hf}_{2}{\rm (S,Te)B}$, by mixing the elements on the A site in the prototypical Cr2AlC-type${\rm Cr}_{2}{\rm AlC\text{-}type}$ MAX-phase crystal structure instead of the more common M site. We have considered thermodynamic, mechanical and electronic properties of the resulting Hf2S1-xTexB${\rm Hf}_{2}{\rm S}_{1-x}{\rm Te}_{x}{\rm B}$ alloy system in the entire composition range, 0 <= x <= 1$0 \le x \le 1$. With increasing Te content, the modulus of elasticity and hardness show a decreasing trend, while the material retains its electrical conductivity. Further analysis of the optical properties shows that the studied solid solutions are good candidates for effective absorbing materials in the UV region. Our study indicates that strategic alloying within the A site of MAB phases can selectively tailor certain material properties while preserving their favorable electrical and mechanical performance.