"Advancing on" is a phrase that indicates movement towards a particular destination or goal. Some synonyms for this phrase include "moving towards," "closing in on," "proceeding towards," "approaching," "coming closer to," "edging closer to," "heading towards," or "making strides towards." These terms all suggest progression towards a specific objective, whether physical, mental, or emotional. They can be used in a variety of settings, from discussing military tactics to describing personal growth. Whatever the context, these synonyms convey a sense of purposeful movement towards a desired outcome.