On 20 October 2020, Pope Francis named Burnette as apostolic administrator of the former Slovak Catholic Eparchy of Saints Cyril and Methodius of Toronto.[3][4] On 3 March, 2022, Pope Francis changed the jurisdiction and circumscription of the eparchy to establish the Exarchate of Saints Cyril and Methodius of Toronto. Burnette was appointed apostolic administrator of this new exarchate.[5]
In January 23, 2023, Burnette was appointed as apostolic administrator of both the Eparchy of Parma and the Eparchy of Phoenix.[6] These appointments, noted as being temporary, made Burnette the leader of over half of the Byzantine Catholic eparchies worldwide, until the appointment of Robert Mark Pipta as eparch of Parma.[7]