Multi-intent spoken language understanding remains challenging due to the scarcity of labeled data and the complexity of modeling intent-slot correlations. In this paper, we propose Collaborative Self-Distillation (Colla-SD), a novel framework that leverages a pair of open-weight large language models (LLMs) to synthesize high-quality labeled samples, which are used for fine-tuning the LLMs to achieve self-distillation. Our approach consists of six stages: (a) intent-slot sampling, (b) reverse progressive skeleton generation, (c) deduplication and quality filtering, (d) cross-model consensus flagging, (e) adjudication of disagreements, and (f) model training. Evaluations on the test sets of public benchmarks show that Colla-SD dramatically improves the open-weight LLM’s overall accuracy by up to 13 times. Equipped with Colla-SD, 7B/8B open-weight models achieve up to 62.68% intent accuracy and 66.13% slot F1 on MixATIS, even outperforming massive open-source and commercial LLMs while also enabling full joint prediction. Ablation studies confirm that each component of our method is critical for the quality of synthesized data, and further analysis reveals that our method can generalize to diverse LLM architectures. Our work demonstrates that Colla-SD can effectively bridge the gap between LLM generation and zero-shot structured semantic parsing.