Formal:
* Besought: This implies a strong and earnest plea.
* Implored: This suggests a desperate or urgent request.
* Supplicated: This emphasizes humility and a sense of dependence on the person being entreated.
* Plead: This suggests a formal or legal appeal.
* Solicited: This implies a request for something specific, often a favor.
Informal:
* Begged: This is a simple and direct synonym.
* Prayed: This suggests a very strong desire for something.
* Asked earnestly: This emphasizes the sincerity of the request.
* Urged: This implies a strong recommendation or persuasion.
* Requested with urgency: This focuses on the importance of the request.
The best synonym for "entreated" will depend on the specific context of your writing.