Due to the COVID-19 pandemic, global supply chains have experienced sustained impacts from unprecedented complex disruptions in different combinations and at different times. From an efficiency perspective, do these complex supply chain disruptions call for more complex risk management strategies? To answer this, we built an empirically grounded discrete event simulation model, the results of which were analyzed using data envelopment analysis. Results show that with unprecedented complex disruption patterns, a multi-strategy portfolio approach is usually less efficient than a single-strategy or a do-nothing approach unless the strategy portfolio has certain characteristics. The most efficient strategy portfolios typically consist of a moderate number of diverse strategies. Too many strategies in a portfolio can be problematic, leading to increased costs that outpace improvement in revenue and service level. Results illustrate that even a strategy that generally performs poorly can be part of a very good strategy portfolio and vice versa. This study provides nuanced and novel findings that contribute to the resolution of the literature debate about the value of multi-strategy portfolios in addressing complex disruption patterns. Highlighting the value of a strategy portfolio view, these insights help firms better prepare for the next complex and sustained global supply chain disruptions.