The impact of nanoparticle size effects in heterogeneous catalytic kinetics over supported metal catalysts is discussed for clusters having several distinct active sites. Theoretical analysis demonstrates that considerations of different activity for such sites not only allow a description of a smooth increase or decrease of turnover frequency as a function of cluster size, but also can in principle account for maxima in turnover frequency. Several examples are presented addressing advantages and shortcomings of the model (in some cases giving physically unreasonable values of parameters during numerical data fitting). Comparison with a rival model with a continuous variation of activity is presented.