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Although reasoning is innately language-agnostic, the multilingual capacities remains a significant challenge for large language models (LLMs). Their ability to generate structured, step-wise explanations is constantly restricted to dominant languages in pre-training data, making cross-lingual generalisation difficult and hindering broader global adoption. Recent works have introduced eclectic strategies to improve reasoning beyond English; however, these methods remain related to specific language that is not always optimal for reasoning.To improve LLMs’ multilingual reasoning abilities, we propose a modular approach that instructs the models to structure reasoning passages in a different problem space and then self-refine their capabilities to deliver step-wise reasoning passages that lead to the solution. Experiments show that our approach stably achieves significant improvements in the multilingual reasoning of various models and task, with improved reasoning consistency across languages.