At the 39th Chess Olympiad held at Khanty-Mansiysk in 2010, Torre manned Board 4 for the Philippines and played 7 games where he scored 4½ points with 3 wins, 3 draws and 1 loss with a performance rating of 2460 which was a shade below his Elo rating of 2489. In 2012, Torre participated in his record 21st Olympiad appearance at the 40th Chess Olympiad breaking his tie with Lajos Portisch held at Istanbul, Turkey. He manned Board 3 in this edition of the Olympiad. He scored 3½ points in 7 games on the strength of 2 wins, 3 draws and 2 losses. He recorded a very high performance rating of 2611 in this Olympiad, higher than his 2469 Elo rating. In 2014, Torre again manned Board 3 for Team Philippines in the 2014 Tromso Olympiad for his record-setting 22nd appearance in the said tournament. He scored 5½ points in 9 games posting 3 wins, 5 draws against a solitary loss. He recorded a performance rating of 2527 and gained 9.9 Elo points in the said Olympiad. His Elo rating then was 2438.