There are several synonyms for the phrase "more rapidly." These include quickly, swiftly, speedily, hastily, briskly, expeditiously, and prompt. All of these terms convey a sense of urgency and a need for speed. "Quickly" and "swiftly" emphasize the speed at which something is happening, while "speedily" and "hastily" suggest a sense of urgency or a need to act fast. "Briskly" implies a quick and energetic pace, while "expeditiously" and "prompt" indicate a need for efficiency and timeliness. Ultimately, the choice of synonym will depend on the context and tone of the sentence.