There are several synonyms for the phrase "become involved in", each carrying a different connotation. For instance, "participate in" suggests active engagement, while "engage in" implies a less committed level of involvement. "Join in" pertains to joining a pre-existing activity or group, while "get involved in" emphasizes the initiation of the involvement. Alternatives such as "immerse oneself in", "embark on" and "take part in" also exist. The choice of words depends on the nature of the situation and the writer's intended emphasis. Nonetheless, all these synonyms evoke a sense of active involvement with a particular activity, event, or group.