Automatic search for Multi-Agent Systems has recently emerged as a key focus in agentic AI research. Several prior approaches have relied on LLM-based free-form search over the code space. In this work, we propose a more structured framework that explores the same space through a fixed set of composable components. We show that, despite lacking the generative flexibility of LLMs during the candidate generation stage, our method outperforms prior approaches on a majority of evaluated benchmarks across two backbone LLMs and two domains: mathematics and question answering. Furthermore, our method offers additional advantages, including a more cost-efficient search process and the generation of modular, interpretable multi-agent systems.