Bacterial cells contain many large, spatially extended assemblies of ions, molecules, and macromolecules, called hyperstructures, that are implicated in functions that range from DNA replication and cell division to chemotaxis and secretion. Interactions between these hyperstructures would create a level of organization intermediate between macromolecules and the cell itself. To explore this level, a taxonomy is needed. Here, we describe classification criteria based on the form of the hyperstructure and on the processes responsible for this form. These processes include those dependent on coupled transcription-translation, protein-protein affinities, chromosome site-binding by protein, and membrane structures. Various combinations of processes determine the formation, maturation, and demise of many hyperstructures that therefore follow a trajectory within the space of classification by form/process. Hence a taxonomy by trajectory may be desirable. Finally, we suggest that working toward a taxonomy based on speculative interactions between hyperstructures promises most insight into life at this level.