There are various synonyms that can be used instead of the commonly used phrase "move on." One such synonym is "progress," which means to advance or develop in a positive manner. Another option is "shift," which refers to a change or transition from one state or position to another. "Elevate" is another apt synonym for "move on," which suggests moving to a higher level or standard. Other suitable options include "advance," "proceed," and "continue," all of which convey the idea of moving forward or ahead. Ultimately, the choice of synonym depends on the context and the writer's intent, but these options can offer a variety of viable alternatives for expressing the notion of moving on.