Words:
* Entreat: To ask earnestly or urgently.
* Beseech: To ask for something in a serious and sincere way.
* Solicit: To ask for something in a formal way.
* Implore: To beg someone to do something.
Phrases:
* Humbly request: This emphasizes the humility of the request.
* Politely inquire: Highlights the gentle and respectful nature of the question.
* With deference, ask: Shows respect and acknowledges the other person's authority.
* Would it be possible to... Creates a softer and more indirect way of asking.
The best word or phrase to use will depend on the specific context and the tone you want to convey.