Any clinical decision support (CDS) design project integrating computational technologies with clinician workflows will require the merging of multiple perspectives and fields of expertise in multidisciplinary teams. Much like the tools these teams aim to create, the team itself will need to continuously build, monitor, and repair a mutually beneficial relationship between each of its members. From our experience during the early development stages of an AI-enabled CDS tool for hospital-acquired infection (HAI) prevention, we abstract three central tenets of a symbiotic design process we have found to be vital for aligning goals, priorities, mental models, and techniques among a multidisciplinary team: (1) recurrent bottom-up feedback, (2) continual model (re-)alignment, and (3) openness to co-direction. With regards to these tenets, we discuss the successes and challenges our team has faced during the symbiotic design process through a series of vignettes and how these experiences coalescing diverse human design teams can influence the design of human-machine teams.