Anomaly detection is a crucial problem in data mining and analytics with widespread applications. Existing studies, however, often treat all anomalies equally, overlooking the fact that in many real-world scenarios, anomalies can have varying levels of importance. In this paper, we consider priority-aware anomaly detection. A key challenge in this problem is the overlap between marginal unlabeled instances and anomalies, which leads to high false-positive rates. Most existing models focus on distinguishing between normal and abnormal instances, largely neglecting the potential to distinguish marginal unlabeled data from anomalies. To address this issue, we propose EdgeBoost4PAD (EBPAD), an adaptive strategy that aims to increase the separation between marginal unlabeled instances and labeled anomalies, thus enhancing a model's ability to learn a more discriminative and robust decision boundary. We generalize a distance-based instance partitioning approach to make EBPAD applicable to various semi-supervised anomaly detection models operating in both score and representation spaces. The experimental results demonstrate that EBPAD consistently improves the performance of different anomaly detection models across diverse datasets and settings, yielding average increases of 7% in AUROC and 38.7% in AUPRC under the priority-aware anomaly detection setting. In addition, EBPAD also attains average improvements of 6.4% in AUROC and 36.5% in AUPRC under the priority-unaware setting.