"Becomes involved" is a common phrase used to describe a person's participation or engagement in an activity, task, or situation. There are a variety of synonyms that may be used to convey this meaning more effectively, such as "engages," "participates," and "enters into." Other potential synonyms might include "involves oneself," "takes part in," or "joins in." Depending on the context and tone of the sentence, different words may be more appropriate. For example, "enters into" could represent a more formal or deliberate type of involvement, while "joins in" might be more casual or lighthearted. Regardless of the choice of synonym, it's important to accurately convey the intended meaning in order to effectively communicate with readers or listeners.