There are a plethora of synonyms for the phrase "over the border". Some of the most commonly used include "across the border", "past the border", "beyond the border" and "through the border". Other options include "crossing the border", "transcending the border" and "crossing over". When discussing international travel, one might say "entering another country", "leaving the country" or "going abroad". Additionally, "over the line", "crossing the line" and "breaking the boundary" can be used in more metaphorical or abstract contexts. Regardless of the specific phrasing used, all of these synonyms imply a crossing from one location or jurisdiction to another.