Abstract: More than 300 million people worldwide are affected by one of over 7,000 known rare diseases, yet diagnosis remains difficult because patients initially present with incomplete and heterogeneous phenotypes. We present HPOQuest, a training-free framework for sequential phenotype acquisition in rare-disease diagnosis. Starting from a small set of observed patient phenotypes, HPOQuest maintains a probabilistic disease ranking and iteratively selects informative follow-up questions to support clinicians during patient assessment. Confirmed phenotypes update the disease ranking, while all responses update the candidate question set. Across four benchmark cohorts, HPOQuest substantially improves diagnosis from sparse initial phenotypes, with gains of up to 30% points at Recall@1 and 45% points at Recall@5. These results demonstrate that sequential phenotype acquisition can substantially improve rare-disease diagnosis from limited initial clinical evidence.