Large language models (LLMs) are essential in natural language processing (NLP) but are costly in data collection, pre-training, fine-tuning, and inference. Task-specific small language models (SLMs) offer a cheaper alternative but lack robustness and generalization. This paper proposes LEGO, a novel technique to extract SLMs from an LLM and recombine them. Using state-of-the-art LLM pruning strategies, we can create task- and user-specific SLM building blocks that are efficient for fine-tuning and inference while also preserving user data privacy. LEGO utilizes Federated Learning and a novel aggregation scheme for the LLM reconstruction, maintaining robustness without high costs and preserving user data privacy. We experimentally demonstrate the versatility of LEGO, showing its ability to enable model heterogeneity and mitigate the effects of data heterogeneity while maintaining LLM robustness.