Structured knowledge bases are an increasingly important way for storing and retrieving information. Within such knowledge bases, an important search task is finding similar entities based on one or more example entities. We present QBEES, a novel framework for defining entity similarity based on structural features, so-called aspects and maximal aspects of the entities, that naturally model potential interest profiles of a user submitting an ambiguous query. Our approach based on maximal aspects provides natural diversity awareness and includes query-dependent and query-independent entity ranking components. We present evaluation results with a number of existing entity list completion benchmarks, comparing to several state-of-the-art baselines.