When it comes to an "application request" or a formal plea for a certain service or permission, there are several synonyms that one can use to express their desired message. One of the most common options is to use the word "petition" which refers to a document requesting legal action. Another option is the word "solicitation" which refers to a formal request for a donation or assistance. One can also use other words such as "proposal", "submission", "appeal", and "inquiry". Overall, choosing the right synonym for an application request can make all the difference in communicating your message effectively.