IOTL, John Tzimiskes died at a very inconvenient time for the Empire. Fatimid Egypt was having difficulty establishing herself in Syria, and the Hamdanids and the Buyids were upon the brink of war. How might John Tzimiskes' continued existence, and the consequent lack of civil war, affect matters? Might Byzantium be able to take Jerusalem? How would it affect the gradual annexation of Transcaucasia, as David of Tao, one of the first sovereigns to bequeath his kingdom to the Empire, was pressured into doing so by Basil II, as a punishment for selecting the wrong side during the civil war?