Best-reply search (brs) is a new search technique for game-tree search in multi-player games. In brs, the exponentially many possibilities that can be considered by opponent players is flattened so that only a single move, the best one among all opponents, is chosen. Brs has been shown to outperform the classic search techniques in several domains. However, brs may consider invalid game states. In this paper, we improve the brs search technique such that it preserves the proper turn order during the search and does not lead to invalid states. The new technique, brs^+^+, uses the move ordering to select moves at opponent nodes that are not searched. Empirically, we show that brs^+^+ significantly improves the performance of brs in four-player chess, leading to winning 8.3 %–11.1 % more games against the classic techniques max^n^n and paranoid, respectively. When brs^+^+ plays against max^n^n, paranoid, and brs at once, it wins the most games as well.