There are various synonyms for the phrase "make peace offerings." One of the most common is "extend an olive branch," which derives from the practice in ancient Greece of holding a branch of an olive tree as a symbol of peace. Another alternative is "offer a truce," which suggests a cessation of conflict or hostility between two opposing parties. Additionally, "propose a compromise" is a suitable synonym as it implies a willingness to negotiate and find a mutually beneficial solution to a disagreement. Overall, these synonyms all connote the idea of making an effort to reconcile and end a dispute.