The phrase "onward and upward" typically conveys a sense of progress, growth, and moving forward. There are several synonyms that can be used to express a similar sentiment, such as "advancement," "evolution," "development," and "improvement." Other synonyms could include "rise," "ascend," "prosper," "flourish," and "thrive." These words all suggest forward motion and the idea of reaching higher levels of achievement and success. Additionally, phrases like "moving ahead," "forging ahead," and "pressing forward" can be used to express a determination to keep pushing forward and striving towards new goals. Overall, there are many ways to convey the positive message of "onward and upward" in a variety of contexts.