Developing a unified multilingual model has been a long pursuing goal for machine translation. However, existing approaches suffer from performance degradation - a single multilingual model is inferior to separately trained bilingual ones on rich-resource languages. We conjecture that such a phenomenon is due to interference brought by joint training with multiple languages. To accommodate the issue, we propose CIAT, an adapted Transformer model with a small parameter overhead for multilingual machine translation. We evaluate CIAT on multiple benchmark datasets, including IWSLT, OPUS-100, and WMT. Experiments show that the CIAT consistently outperforms strong multilingual baselines on 64 of total 66 language directions, 42 of which have above 0.5 BLEU improvement.