The phrase "make inroads on" means to gradually accomplish or progress towards a goal or objective. There are several synonyms for this phrase that can be used to convey similar meanings. Some of the common synonyms for "make inroads on" include "advance on," "move closer to," "make progress towards," "gain ground on," and "make headway on." These phrases can be used interchangeably to create a more varied and nuanced writing style. Whether you are writing a formal report or an informal blog post, incorporating synonyms for "make inroads on" can help you to convey your ideas and thoughts in a clear and concise way.