Numerous studies have underscored the significant privacy risks associated with various leakage patterns in encrypted data stores. Most existing systems that conceal leakage either (1) incur substantial overheads, (2) focus on specific subsets of leakage patterns, or (3) apply the same security notion across various workloads, thereby impeding the attainment of fine-tuned privacy-efficiency trade-offs. In light of various detrimental leakage patterns, this paper starts with an investigation into which specific leakage patterns require our focus respectively in the contexts of key-value, range-query, and dynamic workloads. Subsequently, we introduce new security notions tailored to the specific privacy requirements of these workloads. Accordingly, we present, SWAT, an efficient construction that progressively enables these workloads, while provably mitigating system-wide leakage via a suite of algorithms with tunable privacy-efficiency trade-offs. We conducted extensive experiments and compiled a detailed result analysis, showing the efficiency of our solution. SWAT is about slower than an encryption-only data store that reveals various leakage patterns and is faster than a trivially zero-leakage solution. Meanwhile, the performance of SWAT remains highly competitive compared to other designs that mitigate specific types of leakage.