Memory disaggregation can potentially allow memory-optimized range indexes such as B+-trees to scale beyond one machine while attaining high hardware utilization and low cost. Designing scalable indexes on disaggregated memory, however, is challenging due to rudimentary caching, unprincipled offloading and excessive inconsistency among servers. This paper proposes DEX, a new scalable B+-tree for memory disaggregation. DEX includes a set of techniques to reduce remote accesses, including logical partitioning, lightweight caching and cost-aware offloading. Our evaluation shows that DEX can outperform the state-of-the-art by 1.7--56.3X, and the advantage remains under various setups, such as cache size and skewness.