The phrase "on and up" often refers to progress or improvement, and there are several synonyms to express this idea. One option is "ascending," which suggests a gradual and steady climb. Another possibility is "prospering," which implies not only progress but also success and flourishing. "Elevating" and "uplifting" both connote a positive direction, and "advancing" implies movement forward toward a goal. "Improving" and "bettering" both suggest enhancement or refinement, while "growing" emphasizes a sense of expansion and development. Ultimately, regardless of the specific word used, "on and up" signifies the desire for improvement and forward movement.