There are many synonyms for the phrase "have an idea." One could say "conceive," "imagine," "brainstorm," "formulate," "think up," "devise," or "come up with." Each of these synonyms has a slightly different connotation - "conceive" might suggest a more abstract or theoretical idea, while "brainstorm" implies a more collaborative or unstructured process. "Formulate" might be used to describe a more deliberate or planned approach to developing an idea, while "think up" might be more casual or spontaneous. Regardless of the specific synonym used, each one suggests the act of generating a new concept or plan, and invites further exploration and development.