Rush orders are characterised by time constraints and organisational priority. They are handled by the supplier with the aim of meeting customer requirements in as limited a timeframe as possible. Rather than focusing on rush orders as a deterministic planning problem, this paper takes an inter-organisational perspective that highlights the complex networked interactions between the supplier and the customers. In this single case study of an advanced sanitary product supplier, rush orders involve process prioritisation concerning both: (i) supplies of in-stock parts that are delivered with pre-set time objectives; and (ii) parts not in stock that must be quickly fabricated. This supply process is highly emergent, in that unexpected events or properties occur. This study considers the difficulties of determining and dealing with root causes, unexpected effects, and interventive solutions for rush orders. This operational level of analysis provides a foundation for advocating the application of complex systems thinking to solve or at least significantly mitigate the problem of rush orders. It also contributes to and advances further research on this subject.