Text style transfer (TST) modifies a source sentence to match a target style while preserving its semantics. While existing models perform well on simple styles like sentiment and formality, they struggle with complex, entangled styles such as poetry and brand-specific tones, which require advanced operations to disentangle content and style. We propose a multi-agent self-check framework that contains a large language model (LLM) as a planner for disentangling subtasks and expert agents for executing the subtasks. This training-free multi-agent framework decomposes TST into manageable components, enabling iterative refinement through a self-check module that balances style adherence and content preservation. Experiments on both simple and complex style datasets show our framework significantly improves style strength and content preservation, with strong adaptability in few-shot settings.