Recent studies have shown that code-switching data (CSD), in which multiple languages are mixed within the same context, can improve cross-lingual transfer and multilingual alignment in large language models (LLMs). Recent studies on synthetic code-switching for LLMs have primarily focused on bilingual transfer between English and a target language, leaving instruction-tuning settings that jointly mix three or more languages within each example largely unexplored. In this work, we investigate multilingual code-switching instruction tuning across four languages: English, Japanese, Korean, and Chinese. We evaluate multilingual understanding on Belebele and MMLU. Our experiments show that simple sentence-level multilingual CSD consistently improves the four-language average accuracy across all bilingual, trilingual, and quadrilingual settings for Gemma-2-2B, indicating that multilingual code-switching can be effective beyond bilingual transfer settings.