An adaptive external sorting algorithm is proposed where individual sorts vary the amount of memory, they use during their lifetimes based on both the availability of memory and the needs of the sort. Algorithms for allocating memory among multiple concurrent instances of this algorithm are also investigated. Most previous work in this area has investigated how to partition memory among queries that receive a static memory allocation when they begin. Other work has investigated adaptive algorithms but has not considered strategies for partitioning memory among multiple concurrent instances of queries based on these algorithms.