Although the Supplemental Instruction (SI) model is offered in a wide range of contexts across many educational institutions in 29 countries, it maintains an identifiable essence. Each SI program, known in Australia as PASS, tends to operate autonomously within its particular institution while maintaining some of the features that interlink all programs that formally identify with this model. These features include near peers facilitating collaborative learning situations that improve attendees' learning outcomes and increase retention. This paper suggests that complexity theory provides a useful conceptual lens for analysing this multifaceted and multilayered peer learning model. Dimensions of complexity such as self-organisation, fractality, dynamism and emergence seem to offer ways of seeing and sense making that can enhance our understanding of the SI/PASS model, both organisationally and pedagogically. In this initial exploration of complexity and SI/PASS, particularly in its organisational features, I hope to foster conversations that will consider the implications and opportunities of seeing this particular peer learning approach as self-organising, dynamic and emergent.