Hello to all alternate historians,
I took inspiration from Mathalamus' Byzantine Empire Enduring TL, and this is my timeline. It will be made in installments. I'll try to avoid Byzantine cliches. Don't worry, it wont turn into a Byzant-wank.
I decided to make the POD 871, where Basil I's eldest son Constantine doesn't die (he later becomes the Emperor, and is better than Leo the 'Wise'. The rest of Basil's reign is very similar to OTL, so the timeline starts at his death. (BTW, with names, I'll use the Greek form if possible (although obviously in the Latin script. For example, John will become Ioannis. If there are any Greeks reading this, please correct any misspellings.)
Chapter I: Konstantinos
After Basil I's unfortunate death in 886, his son Konstantinos (now the VII) rose to the throne. His younger (possibly half-)brother became a scholar and a writer. Konstantinos' first act as Emperor was to reform the army, making the regular army more effective by creating a new formation, which focused on the use of phalanx-like pikemen in the center, with more elite troops armed with swords or axes on the sides, and Kataphraktoi on the far wings. Konstantinos sent a large army to the Byzantine enclaves in Eastern Sicily, which rebuffed a Sicilian Arab army at the battle of Tauromenion. The new formation worked just as designed, with the Arabs attacking the Byzantine centre, applying most of their forces there in an attempt to break the line. The sides, formed mostly of experienced former Hikanatoi, enveloped the Arab wings. The Kataphraktoi had defeated the lighter Arab cavalry, and smashed into the rear of the Arab forces. An envelopment that effective had not been seen since Carrhae. The entire Arab forces were killed or captured. This was the decisive battle in the Reconquest of Sikelia. Messina was recaptured in 911, Syracuse in 914 and the Arabs were expelled entirely in 921.
Meanwhile, Konstantinos decided to keep Bulgarian trade at Constantinople until he was finished in Sicily. An economic issue he had though was starvation in some areas due to a famine. The few harvested crops were sent to the soldiers in Sicily and the citizens of Constantinople. Revolts in Epirus were put down forcefully, but Konstantinos realised that his empire needed some better land for crop cultivation. While Konstantinos had his eyes on Egypt, he realised that an easier target was the rising Fatimid Caliphate in the Maghreb. What is now Tunisia and Algeria were once the breadbasket of the Roman empire before the conquest of Egypt. The grain supply of these regions would be adequate. After the conquest of Sicily, Konstantinos sent a fleet to raid the Fatimids' coastal towns. The first major army was sent to the land at the beginning of the peninsula, cutting off Carthage from the rest of Tunisia. A fleet interdicted grain supplies coming into the city. After a very nearly successful break in attempt by Fatimid forces, the Byzantines, commanded personally by Konstantinos, decided to emulate the tactics of Julius Caesar, erecting double walls around the peninsula to intercept any forces attempting to get in or out of the city. The city held out for a suprisingly long time, until a 'diplomat' was sent into the city on behalf of Konstantinos. The leader of the Fatimids, Abdullah al-Mahdi Billah, met him in Constantinople. Despite the presence of many Arab bodyguards, the Byzantine 'diplomat' managed to stab the Caliph in the side with a hidden dagger. The would-be assassin was immediately executed. Abdullah's wounds were bandaged, but the poison on the blade caused an infection which lead to the Caliph's death in 928. After the death of the Caliph, different factions in the city succumbed to infighting, with different factions fighting turf wars with armed gangs of former soldiers or criminals. In the night of September 17th, the gates of Carthage were opened by a faction, led by Ahmed 'al-Ghazi' Nur, which believed it would become governors of Carthage in the event of a Byzantine conquest if they helped. Ahmed was crucified as an insult to him. He later became a martyr to Shi'ites, unaware of his racketeering prior to the Byzantine conquest. The Byzantines had retaken Carthage, but all of the Maghreb was not in Konstantinos' hands yet.