There are several synonyms for the phrase "making off the top of one's head." Some of them include "winging it," "improvising," "ad-libbing," "spontaneously," "off the cuff," and "thinking on one's feet." All of these phrases have a similar meaning, which implies that one is speaking or acting without much prior planning or preparation. It can also suggest that someone is relying on their instincts or intuition to solve a problem or create something new. While there is some risk involved in this type of approach, it can also lead to creative and innovative solutions that might not have been possible otherwise.