Currently, research on artificial intelligence model copyright protection primarily focuses on the robustness of watermarking techniques and the enhancement of model accuracy, while model traceability remains relatively under explored. To address the challenge of tracking piracy in multi-user environments, a model fingerprinting framework enabling piracy traceability is proposed. In this framework, a unique and controllable data augmentation combination is randomly assigned to each user, based on which a traceable fingerprint set is generated. Multi-task learning techniques are then employed to simultaneously retrain the source model and the traceability model, which receives outputs from the source model, using the fingerprint sets. After retraining, the source model is transformed into a user-specific model with embedded features from the unique fingerprint set. The traceability model is capable of inferring the corresponding user based on the prediction results of the fingerprint set from the respective proprietary model. This approach maintains a balance between traceability effectiveness and the performance of proprietary models. Experimental results on the CIFAR10 and Fashion-MNIST datasets demonstrate that the proposed method achieves over 90% accuracy in both piracy detection and traceability tasks, confirming its effectiveness across various task scenarios.