There are several synonyms for the phrase "not by a great deal". Some alternatives include "not much", "barely", "scarcely", "hardly", "just a tad", "slightly", "marginally", "minimally", "negligibly", and "insignificantly". These expressions can be used to convey a slight difference or lack of change in a situation, such as "The new recipe isn't much better than the old one" or "She barely passed her driving test". By using synonyms, writers and speakers can add variety to their language and avoid repetition. It also helps in communicating the degree of change, which can be important in conveying a message accurately.