Dealing with unforeseeable changing situations, often seen in exploratory and hazardous task domains, requires systems that can adapt to changing tasks and varying environments. The challenge for engineering design researchers and practitioners is how to design such adaptive systems. Taking advantage of the flexibility of multi-agent systems, a self-organizing systems approach has been proposed, in which mechanical cells or agents organize themselves as the environment and tasks change based on a set of predefined rules. To enable self-organizing systems to perform more realistic tasks, a two-field framework is introduced to capture task complexity and agent behaviors, and a rule-based social structuring mechanism is proposed to facilitate self-organizing for better performance. Computer simulation-based case studies were carried out to investigate how social structuring among agents, together with the size of agent population, can influence self-organizing system performance in the face of increasing task complexity. The simulation results provide design insights into task-driven social structures and their effect on the behavior and performance of self-organizing systems.