A growing number of applications depend on Machine Learning (ML) functionality and benefits from both higher quality ML predictions and better timeliness (latency) at the same time. A growing body of research in computer architecture, ML, and systems software literature focuses on reaching better latency/accuracy tradeoffs for ML models. Efforts include compression, quantization, pruning, early-exit models, mixed DNN precision, as well as ML inference accelerator designs that minimize latency and energy, while preserving delivered accuracy. All of them, however, yield improvements for a single static point in the latency/accuracy tradeoff space. We make a case for applications that operate in dynamically changing deployment scenarios, where no single static point is optimal. We draw on a recently proposed weight-shared SuperNet mechanism to enable serving a stream of queries that uses (activates) different SubNets within this weight-shared construct. This creates an opportunity to exploit the inherent temporal locality with our proposed SubGraph Stationary (SGS) optimization. We take a hardware-software co-design approach with a real implementation of SGS in SushiAccel and the implementation of a software scheduler SushiSched controlling which SubNets to serve and what to cache in real-time. Combined, they are vertically integrated into SUSHI—an inference serving stack. For the stream of queries SUSHI yields up to 25% improvement in latency, 0.98% increase in served accuracy. SUSHI can achieve up to 78.7% off-chip energy savings.