There are several synonyms suitable to use instead of the phrase "met halfway," which refers to finding a compromise point between two parties. One of the most common equivalents is "reached a middle ground," emphasizing the place where both sides agree. Another synonym is "found a happy medium," where each party gives in a bit to reach a mutually satisfying outcome. Additionally, "conceded some ground" describes how each party compromises on their positions to make progress towards a solution. Similarly, "compromised" signifies that both sides sacrifice something to reach a mutually beneficial agreement. These synonyms, among others, are useful for expressing the idea of meeting halfway in various situations.