The concept of stoichiometrically unique reactions (response reactions, RERs) is extended to the group additivity (GA) methods. Namely, it is shown that the main assumption of the GA methods according to which chemical species may be "constructed" from a specified number and type of structural units, or groups, may be formally appended to the conventional RER formalism. As a result, one can define and generate a stoichiometrically unique class of GA RERs. Several properties and applications of the newly defined GA RERs are pointed out. In particular, it is proved that the stoichiometry and thermodynamic functions of the GA RERs are interrelated in a simple manner with the error of the GA methods. This finding is used to reformulate the GA methods alternatively (and equivalently), in terms of GA RERs.