Why exactly would the Byzantines win these conflicts in Naples, Sicily or Italy? They will be facing many foes who are on the defensive. Byzantium has an extensive empire as it stands, is it in their best interest to conquer all the way up to the Alps? Putting aside that it is very unlikely to occur, and with a tl in the 11th, we still have the Saljuqs and the Byzantine excesses against their Armenian subjects and the betrayals and schemes of Anatolian nobility and the imperial bureaucracy. Byzantium is decaying at its root already and is not the same power that defeated Umar al-Aqta in 869 or who made gains against the Abbasid Caliphate through the 10th century.
Byzantium would do well to focus on its east and south. European adventurism makes little sense except after pacifying Saljuq, Fatimid and Abbasid threats and this expansion should possibly limited to Sicily, to avoid breaching the balance of power and staying outside the domain of the Holy Roman Empire.