Data visualization made of multiple visualization techniques, e.g., dashboards and small multiples, is taking the scene as data, AI algorithms and their analysis are becoming more complex and articulated. However, still too little is said about what are the core dimensions of these interactions that may contribute to characterize visualization techniques orchestration in scenarios where humans and AI work together and communicate through visual languages, and what is the differential in complexity with respect to single charts interaction. Depending on such dimensions, their level, and their combination, interaction may require a cognitively growing effort. The present study aims at giving a unified view of complex visual frameworks in order to identify the invariants of visualization techniques characterization, and proposes a group of necessary and sufficient dimensions emerging when visualization techniques are the focus of the design and may be the focus of interaction between humans and AI. The paper identifies and discusses these dimensions, starting from the literature, and giving a characterization of each of them in terms of constituent levels. The framework may be applied to analysis of a range of data visualization tools and approaches, towards their concrete application to a distributed visual cognition framework where humans-AI interactions will take place.