As large language models (LLMs) grow in sophistication, some of their capabilities surpass human abilities, making it essential to ensure their alignment with human values and intentions, i.e., Superalignment. This superalignment challenge is particularly critical for complex tasks, as annotations provided by humans, as weak supervisors, may be overly simplistic, incomplete, or incorrect. Previous work has demonstrated the potential of training a strong model using the weak dataset generated by a weak model as weak supervision. However, these studies have been limited to a single capability. In this work, we conduct extensive experiments to investigate weak to strong generalization for LLMs with multi-capabilities. The experiments reveal that different capabilities tend to remain relatively independent in this generalization, and the effectiveness of weak supervision is significantly impacted by the quality and diversity of the weak datasets. Moreover, the self-bootstrapping of the strong model leads to performance degradation due to its overconfidence and the limited diversity of its generated dataset. To address these issues, we proposed a novel training framework using reward models to select valuable data, thereby providing weak supervision for strong model training. In addition, we propose a two-stage training method on both weak and selected datasets to train the strong model. Experimental results demonstrate our method significantly improves the weak to strong generalization with multi-capabilities.