The term 'take off on' can be defined as to IMITATE or copy someone or something. This can be done in a variety of ways, such as mimicking, riffing, imitating, or aping. Mimicking is the act of copying someone's behavior or mannerisms, while riffing is the act of improvising or creating something new based on an existing idea. Imitating is the act of copying someone's actions or words, and aping is the act of copying someone's style or mannerisms. All of these activities are forms of taking off on someone or something.