Technological processes, reconstructed from the archaeological record, are used to study the evolution of behaviour and cognition of Neanderthals and early modern humans. In comparisons, technologies that are more complex infer more complex behaviour and cognition. The manufacture of birch bark tar adhesives is regarded as particularly telling and often features in debates about Neanderthal cognition. One method of tar production, the ‘condensation technique’, demonstrates a pathway for Neanderthals to have discovered birch bark tar. However, to improve on the relatively low yield, and to turn tar into a perennial innovation, this method likely needed to be scaled up. Yet, it is currently unknown how scaling Palaeolithic technological processes influences their complexity. We used Petri net models and the Extended Cyclomatic Metric to measure system complexity of birch tar production with a single and three concurrent condensation assemblies. Our results show that changing the number of concurrent tar production assemblies substantially increases the measured complexity. This has potential implications on the behavioural and cognitive capacities required by Neanderthals, such as an increase in cooperation or inhibition control.