An all-k-nearest-neighbor (AkNN) query finds k nearest neighbors for each query object. This problem arises naturally in many areas, such as GIS (geographic information system), multimedia retrieval, and recommender systems. To support various data types and flexible distance metrics involved in real applications, we study AkNN retrieval in metric spaces, namely, metric AkNN (MAkNN) search. Consider that the underlying indexes on the query set and the object set may not exist, which is natural in many scenarios. For example, the query set and the object set could be the results of other queries, and thus, the underlying indexes cannot be built in advance. To support MAkNN search on datasets without any underlying index, we propose an e?cient disk-based algorithm, termed as Partition-Based MAkNN Algorithm (PMA), which follows a partition-search framework and employs a series of pruning rules for accelerating the search. In addition, we extend our techniques to tackle an interesting variant of MAkNN queries, i.e., metric self-AkNN (MSAkNN) search, where the query set is identical to the object set. Extensive experiments using both real and synthetic datasets demonstrate the effectiveness of our pruning rules and the e?ciency of the proposed algorithms, compared with state-of-the-art MAkNN and MSAkNN algorithms.