The phrase "grow into" is commonly used to describe a process of developing or maturing over time. There are several synonyms that can be used to convey a similar meaning, depending on the context. For instance, "evolve into" suggests a gradual transformation or change, while "mature into" implies a process of reaching a certain level of development or understanding. Other synonyms include "develop into," "progress into," "transform into," and "morph into." Ultimately, the choice of synonym will depend on the nuances of the sentence and the desired connotation.