While physical visualizations have existed for many years, most of them remain monolithic and static. We identify a promising category of physical visualizations we call composite physical visualizations. Composite physical visualizations are combinations of multiple physical objects and can be designed to better leverage both human and technological capabilities. We show that two important properties have to be considered when designing such visualizations: their level of actuation and their manipulability. Through examples, we illustrate the tradeoffs between these two dimensions, and identify the need for more research in this particular area.