There are numerous synonyms that can be used to express the same sentiment as "beg a favour of." One might say "ask for a favour," "plead for assistance," "implore for help," or "request aid." Alternatively, phrases like "seek assistance," "solicit help," or "call upon for support" might also be used to express the same concept. Whatever terminology one chooses to use, the essential meaning remains the same. It is a request for assistance, usually implying a sense of desperation or urgency. No matter what language is used, the underlying intent remains the same, asking for assistance in a polite and respectful way.