Many cloud service providers employ specialized hardware accelerators, called neural processing units (NPUs), to accelerate deep neural networks (DNNs). An NPU scheduler is responsible for scheduling incoming user requests and required to satisfy the two, often conflicting, optimization goals: maximizing system throughput and satisfying quality-of-service (QoS) constraints (e.g., deadlines) of individual requests. We propose Layerweaver+, a low-cost layer-wise DNN scheduler for NPUs, which provides both high system throughput and minimal QoS violations. For a serving scenario based on the industry-standard MLPerf inference benchmark, Layerweaver+ significantly improves the system throughput by up to 266.7% over the baseline scheduler serving one DNN at a time.