Multiparty private set intersection (MPSI) protocols allow participants to compute the intersection of their datasets while preventing leakage of non-intersecting elements. However, these methods often enforce exact matching, which can be overly restrictive in scenarios where partial intersections provide more meaningful insights. To address this limitation, we introduce a federated learning-enabled threshold multiparty private set intersection (T-MPSI) framework that ensures elements are included in the intersection only if they appear in at least a certain number of datasets. This approach is particularly relevant in cyber threat intelligence sharing and secure data collaboration. Our proposed framework employs federated graph neural networks to dynamically optimize the intersection threshold based on real-time data distributions. We integrate homomorphic encryption to enhance privacy while minimizing communication and computational costs. To evaluate the effectiveness of our method, we conducted simulations in three client population scenarios, comparing against popular protocols. Our results show that our approach achieves lower computation overhead, better intersection accuracy, and scalable performance, making it a viable solution for large-scale privacy-preserving applications.