Large language models (LLMs) have shown remarkable progress in encoding clinical knowledge and responding to complex medical queries with appropriate clinical reasoning. However, their applicability in subspecialist or complex medical settings remains underexplored. In this work, we probe the performance of AMIE, a research conversational diagnostic AI system, in the subspecialist domain of breast oncology care without specific fine-tuning to this challenging domain. To perform this evaluation, we curated a set of 50 synthetic breast cancer vignettes representing a range of treatment-naive and treatment-refractory cases and mirroring the key information available to a multidisciplinary tumor board for decision-making (openly released with this work). We developed a detailed clinical rubric for evaluating management plans, including axes such as the quality of case summarization, safety of the proposed care plan, and recommendations for chemotherapy, radiotherapy, surgery and hormonal therapy. To improve performance, we enhanced AMIE with the inference-time ability to perform web search retrieval to gather relevant and up-to-date clinical knowledge and refine its responses with a multi-stage self-critique pipeline. We compare response quality of AMIE with internal medicine trainees, oncology fellows, and general oncology attendings under both automated and specialist clinician evaluations. In our evaluations, AMIE outperformed trainees and fellows demonstrating the potential of the system in this challenging and important domain. We further demonstrate through qualitative examples, how systems such as AMIE might facilitate conversational interactions to assist clinicians in their decision making. However, AMIE's performance was overall inferior to attending oncologists suggesting that further research is needed prior to consideration of prospective uses.