We present MedPI, a high-dimensional benchmark for evaluating large language models (LLMs) in patient-clinician conversations. Unlike single-turn question-answer (QA) benchmarks, MedPI evaluates the medical dialogue across 105 dimensions comprising the medical process, treatment safety, treatment outcomes and doctor-patient communication across a granular, accreditation-aligned rubric. MedPI comprises five layers: (1) Patient Packets (synthetic EHR-like ground truth); (2) an AI Patient instantiated through an LLM with memory and affect; (3) a Task Matrix spanning encounter reasons (e.g. anxiety, pregnancy, wellness checkup) x encounter objectives (e.g. diagnosis, lifestyle advice, medication advice); (4) an Evaluation Framework with 105 dimensions on a 1-4 scale mapped to the Accreditation Council for Graduate Medical Education (ACGME) competencies; and (5) AI Judges that are calibrated, committee-based LLMs providing scores, flags, and evidence-linked rationales. We evaluate 9 flagship models -- Claude Opus 4.1, Claude Sonnet 4, MedGemma, Gemini 2.5 Pro, Llama 3.3 70b Instruct, GPT-5, GPT OSS 120b, o3, Grok-4 -- across 366 AI Patients and 7,097 conversations using a standardized "vanilla clinician" prompt. For all LLMs, we observe low performance across a variety of dimensions, in particular on differential diagnosis. Our work can help guide future use of LLMs for diagnosis and treatment recommendations.