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Efficient management of last level caches (LLCs) plays an important role in bridging the performance gap between processor cores and main memory. This paper is motivated by two key observations, based on our study of LLCs: 1) the capacity demand is highly non-uniform and dynamic at the set level, and 2) neither spatial nor temporal LLC management schemes, working separately as in prior work, can consistently and robustly deliver the best performance under different circumstances. Therefore, we propose a novel adaptive scheme, called STEM, which concurrently and dynamically manages both spatial and temporal dimensions of capacity demands at the set level. In the proposed scheme, a set-level monitor captures the temporal and spatial capacity demands of individual working sets and judiciously pairs off sets with complementary capacity demands so that the underutilized set in each pair can cooperatively cache the other’s victim blocks. The controller also decides on the best temporal sharing patterns for the coupled sets in the event of inter-set space sharing. Further, if the LLC controller cannot find a complementary set for a particular set, STEM can still decide on the best set-level replacement policy for it. Our extensive execution-driven simulation data shows that the proposed scheme performs robustly and consistently well under various conditions.