The phrase "give someone/something the once-over" means to quickly examine someone or something. There are several synonyms that can be used in place of this phrase, including "inspect," "scan," "scrutinize," "survey," and "peruse." While each of these words has its own unique connotations and implications, they all describe a thorough or cursory examination of an object or person. Other possible synonyms might include "assess," "appraise," "evaluate," "examine," or "analyze." Depending on the context, one of these synonyms might be a more appropriate choice than "give someone/something the once-over," or they could be used interchangeably to convey the same meaning.