Distributed monitoring methods address the difficult problem of continuously approximating functions over distributed streams, while minimizing the communication cost. However, existing methods are concerned with the approximation of a single function at a time. Employing these methods to track multiple functions will multiply the communication volume, thus eliminating their advantage in the first place. We introduce a novel approach that can be applied to multiple functions. Our method applies a communication reduction scheme to the set of functions, rather than to each function independently, keeping a low communication volume. Evaluation on several real-world datasets shows that our method can track many functions with reduced communication, in most cases incurring only a negligible increase in communication over distributed approximation of a single function.