Enzyme activity can be modulated by the concurrent action of two modifiers, either activators or inhibitors. The kinetic mechanisms for the interaction of the individual modifiers with the target enzyme can change considerably when two modifiers bind simultaneously. We illustrate a general equation for this kind of interactions, which can unambiguously describe the behavior of activators and inhibitors acting by any combination of classical kinetic mechanisms. The flexibility of this model is exemplified by combinations of activators and/or inhibitors, which can be competitive, uncompetitive or mixed-type, bind the target enzyme in either compulsory or random order, and are able to drive or not enzyme activity to zero at saturation. The model shows that the effects of zero-interaction and synergy between simultaneously acting enzyme modifiers are common events. Yet, in disagreement with previous theories, this model shows that antagonism between enzyme modifiers is a rare effect, which can be predicted only under very particular circumstances.