We introduce the task of entity-centric query refinement. Given an input query whose answer is a (potentially large) collection of entities, the task output is a small set of query refinements meant to assist the user in efficient domain exploration and entity discovery. We propose a method to create a training dataset for this task. For a given input query, we use an existing knowledge base taxonomy as a source of candidate query refinements, and choose a final set of refinements from among these candidates using a search procedure designed to partition the set of entities answering the input query. We demonstrate that our approach identifies refinement sets which human annotators judge to be interesting, comprehensive, and non-redundant. In addition, we find that a text generation model trained on our newly-constructed dataset is able to offer refinements for novel queries not covered by an existing taxonomy. Our code and data are available at https://github.com/google-research/language/tree/master/language/qresp.