以下是一些常见的以engage为动词的短语归纳：

1. Engage in (参与、从事)：参与或从事某项活动、工作或讨论。

例句：She likes to engage in various sports activities.

2. Engage with (交流、互动)：与他人或某个特定对象进行交流、互动。

例句：I enjoy engaging with my audience during presentations.

3. Engage on (讨论、参与)：参与某个特定的话题或讨论。

例句：We should engage on important social issues.

4. Engage with (与…合作)：与某人或某个团体合作或互动。

例句：Our company engages with local communities to support social causes.

5. Engage in conversation (进行对话)：参与或进行对话、交流。

例句：They engaged in a meaningful conversation about their future plans.

6. Engage with customers (与客户互动)：与客户进行互动、交流和提供服务。

例句：The company strives to engage with customers to understand their needs better.

7. Engage with the material (参与到学习材料当中)：全身心地投入到学习或研究材料当中。

例句：He engages with the material by asking questions and taking notes.

这些短语展示了engage在不同语境中的应用，涵盖了参与、交流、合作和学习等方面的含义。