Grow on is a phrase that means to develop a liking for someone or something over time. There are a variety of synonyms that can be used in place of grow on, including become fond of, warm up to, take a liking to, become attached to, get accustomed to, and acclimate to. Each of these phrases conveys the idea of gradually becoming more appreciative of something or someone. Other possible synonyms include become enamored with, come to appreciate, and develop a liking for. No matter what synonym is used, the underlying idea is one of evolving emotions and feelings over time.