The phrase "becoming like" can have various synonyms depending on the context of the sentence. For instance, it can be replaced by "emulating," which means to match or imitate the behavior or qualities of someone or something. Another synonym for becoming like is "assimilating," which refers to the process of adapting to something and taking on its qualities. The word "mirroring" can also be used in this context as it refers to reflecting someone's behavior like a mirror. Lastly, the phrase "adopting the characteristics of" can also be a synonym for becoming like someone or something. Overall, there are several synonyms for the phrase "becoming like," and the most appropriate one depends on the context.