According to Wikipedia's article on Greek-Turkish relations:
"In 2018, declassified documents of the Communist Bulgaria revealed a plan to foment crisis between Turkey and Greece in 1971. The operation codenamed "Cross" and the plan was that Bulgarian secret agents would set fire to the Ecumenical Patriarchate of Constantinople and make it look like the work of Turks. The declassified documents state that “An intervention” in the religious entity would have “significantly damage[d] Turkish-Greek relations and force[d] the United States to choose one side in the ensuing crisis,”. In addition, the Bulgarians also planned to boost the effectiveness of its operation against Greece and Turkey by conducting “active measures" “for putting the enemy in a position of delusion." The plan was developed by the 7th Department of the First Main Directorate of the DS (intelligence and secret police services of communist Bulgaria) and was affirmed by Deputy Head of the Directorate on November 16, 1970, and approved by its Head. The operation was supposed to be prepared by the middle of 1971 and then executed, but it was abandoned."
So what if Bulgaria had gone through with the plan and managed to trigger a Greek-Turkish war? Which side would the US choose?