Parameter-efficient fine-tuning (PEFT) methods optimize large language models (LLMs) by modifying or introducing a small number of parameters to enhance alignment with downstream tasks. However, they can result in catastrophic forgetting, where LLMs prioritize new knowledge at the expense of comprehensive world knowledge. A promising approach to mitigate this issue is to recall prior memories based on the original knowledge. To this end, we propose a model-agnostic PEFT framework, $\textbf{IMSM}$, which $\textbf{I}$nterweaves $\textbf{M}$emories of a $\textbf{S}$iamese Large Language $\textbf{M}$odel. Specifically, our siamese LLM is equipped with an existing PEFT method. Given an incoming query, it generates two distinct memories based on the pre-trained and fine-tuned parameters. IMSM then incorporates an interweaving mechanism that regulates the contributions of both original and enhanced memories when generating the next token. This framework is theoretically applicable to all open-source LLMs and existing PEFT methods. We conduct extensive experiments across various benchmark datasets, evaluating the performance of popular open-source LLMs using the proposed IMSM, in comparison to both classical and leading PEFT methods. Our findings indicate that IMSM maintains comparable time and space efficiency to backbone PEFT methods while significantly improving performance and effectively mitigating catastrophic forgetting. Our code and experimental settings can be accessed through the following link: https://anonymous.4open.science/r/SiameseModels-48D4