The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students working in groups to identify what strategies they employed and how, including what encouraged the opportunities to invoke them. The study revealed behaviours not included in the original taxonomy, including one that we termed "group synergy". We propose extensions to Carlson and Bloom's original taxonomy to encompass group behaviour and identify the importance of these behaviours in developing problem-solving skills. Finally, we suggest improvements for future problem-solving session iterations, with the goal of promoting opportunity for more expert performance.