Recently, the presence of two Kirkendall planes has been discovered in solid-state diffusion couples in various binary metallic systems in our laboratory, and in this work even three Kirkendall marker planes were found in a couple Ti/TiAl3. The bifurcation and trifurcation of the Kirkendall plane can quantitatively be described using the classical diffusion theory in terms of Kirkendall velocity construction. The position of a Kirkendall plane is revealed in the reaction zone not only by inert markers, but also by a different crystal morphology on either side of the plane. A physico-chemical approach is developed which elucidates the role of the Kirkendall effect in the morphogenesis of interdiffusion systems. The occurrence of one or more Kirkendall planes, characterized by morphology changes in the reaction layers, turns out to be related to different nucleation sites of the product grains. The model is demonstrated using the experimental results in the Co¿Si system. It is shown that the predictions using the physico-chemical approach are in good agreement with the experimentally found positions of the Kirkendall plane(s). The presence or absence of inert markers at the Kirkendall planes provides insight into the initial stages of reactive phase formation.