"Budge up" is a common phrase used to ask someone to move over or make space for others. However, there are several synonyms that can be used in different contexts. For instance, "scoot over" is a popular phrase used to ask someone to move or make space. "Shift over" is another synonym that can be used in the same context. "Make way" is another phrase that can be used to ask someone to move out of the way, especially in crowded areas. "Move aside" is another phrase that can be used to request someone to move out of the way. Other synonyms include "clear the path," "step aside," and "move back." All of these synonyms convey a need for someone to move aside to make space for others.