Federated Learning (FL) provides a valuable framework that allows for the collaborative training of models across distributed networks while maintaining the privacy of the data involved. The concept of secure aggregation is crucial in preserving both the privacy and integrity of data within FL systems. However, the deployment of secure aggregation encounters significant barriers. Conventional secure aggregation methods are primarily designed for single-round operations, which can become prohibitively expensive in scenarios that require multiple rounds. Additionally, these methods often struggle in large-scale environments characterized by heterogeneous data and models. This paper introduces the Multiple-Round Aggregation of Abstract Semantics (MRAAS), a novel scheme designed to address the aforementioned limitations in secure aggregation within heterogeneous FL environments. The MRAAS scheme enhances security and reduces the need for extensive data exchanges by aggregating abstracted model semantics instead of raw model gradients, facilitating secure, multiple rounds of aggregation. Key innovations of MRAAS include an advanced abstraction technique, robustness against participant drop-out, and the use of recyclable secrets. These innovations collectively enhance system resilience and reduce the necessity for frequent cryptographic renewals. Our theoretical evaluations focus on the security features of MRAAS. Empirical validations conducted through comparative analyses utilizing two public datasets confirm the superiority of MRAAS.