Press ahead is a phrasal verb that means to continue or proceed with determination, despite difficulties or obstacles. There are several synonyms for this phrase. The first one is to forge ahead, meaning to move forward with force and determination. Another synonym of press ahead is to plough on, which suggests persevering through a tough situation. A third synonym is soldier on, deriving from the military term to carry on despite hardship or danger. Another synonym for press ahead is to push forward, which implies a sense of urgency and perseverance. Finally, one more synonym is to march forward, which indicates a steady, determined progress towards a goal. These synonyms can be used interchangeably to express the idea of pressing ahead with determination.