"Put John Henry on" is a common phrase used to signify asking someone to do a task or take on a responsibility. However, there are several synonyms to this phrase that can be used interchangeably. For instance, you can use "assign John Henry," "delegate to John Henry," "entrust John Henry," "appoint John Henry," "task John Henry," or "allocate to John Henry" to convey the same meaning. These synonyms can be used in different contexts when you need to assign a task to someone, such as at work or in a family setting. Using synonyms for "put John Henry on" can make your language more varied and expressive.