We present an experimental design approach for identifying the optimal levels of the key internal and external environmental conditions of shared leadership, which, in turn, would enable an engineering team to develop and maximise the degree of shared leadership. A full factorial design is applied to evaluate four control factors (shared purpose, social support, voice and external coaching) at two levels and analyse one output metric, defined as 'team centralisation'. Our analysis shows that the four factors are the main contributors to the output metric. However, interactions between the factors are either weak contributors or do not contribute at all to the performance of the output metric. We conclude that having high levels of the three internal team environmental factors and the external coaching environmental condition results in the greatest degree of shared leadership in the senior design environment.