Biases in large language models threaten diagnostic equity and patient safety, and their downstream effects on multi-agent medical systems have only recently been explored. Using a multi-agent framework that mirrored patient-physician conversations, we simulated implicit and cognitive biases within approximately 1,700 MedQA and NEJM encounters and measured downstream effects on diagnostic accuracy, ancillary test utilization, and diagnostic breadth. We found that implicit and cognitive biases could lower diagnostic accuracy by up to 24% and 32%, respectively, with variable effects on test ordering behavior and diagnostic considerations. Our findings expand on current notions of how cognitive and implicit biases may adversely affect multi-agent medical systems, draw parallels between biases in multi-agent systems and real-world clinical contexts, and highlight the need for equitable safeguards in the development of medical agents for clinical decision-making.