The phrase "vying with" can be replaced with a variety of synonyms depending on the context. Some options include competing with, contending with, challenging, rivalling, and striving to surpass. These synonyms all convey a sense of competition or struggle to come out on top in a particular situation. Depending on the specific usage and tone desired, one synonym may be more appropriate than another. For example, "competing with" implies a more equal playing field whereas "challenging" suggests a bolder move. Ultimately, the choice of synonym should be based on the desired effect and the message that the writer wants to convey.