There are many synonyms for the phrase 'by a great deal'. Some possible alternatives include 'significantly', 'considerably', 'substantially', 'enormously', 'vastly', 'markedly', 'noticeably', 'immensely', 'largely', and 'densely'. Each of these words conveys a sense of magnitude and impact, and they can be used to describe a wide range of situations, from financial transactions to emotional experiences. Depending on the context in which they are used, different synonyms may be more appropriate or effective. However, all of these words are useful ways to convey the idea of a significant, impactful change or difference.