The phrase "making demands on" can be replaced with various synonyms depending on the context. One alternative could be "placing expectations on," which carries a similar connotation of expecting a specific result. Another option is "requiring," which indicates a necessary action or obligation. "Pressuring" or "demanding compliance" both convey a sense of assertiveness or even aggression in asking for something. "Asking for" or "requesting" are softer versions that imply a willingness to receive an answer that may not be favorable. Ultimately, the choice of synonym depends on the degree of urgency or force behind the request and the desired tone of the message.