This was roughly Alex’s empire at its peak, from Greece to modern day China. Now Alexander had plans to conquer Italy, Arabia, and North Africa. So let’s assume he succeeds in these conquests. Let’s also assume he conquers Bithniya and Pontus in Anatolia and the Caucauses.
Light blue are his conquests.
Next, Alexander invades the Iberian tribes and the Balkan kingdoms. Then he invades the Greek colonies scattered across Crimea and the Black Sea. He connects Italy by land to the rest of his empire.
Now he sets his sights back on Asia. He’ll leave the Nanda Dynasty in India alone for now, and will instead attack the Iranian tribes of Central Asia.
Then, Alexander gains word that an alliance between the Berber Libyan tribes the Nubian kingdom of Meroe has invaded Egypt. He immediately mobiles a vast army to conquer the two nations. After he conquers Libya and Meroe, he learns of the African states of Punt and Axum near the Red Sea. He immediately mobilizes an army to conquer them. This army also crosses the Red Sea and conquers the Sabaean civilization in Yemen.
Then, Alexander hears word that North India is in turmoil. The western half of the Nanda Dynasty has seceded from the empire. The kings and lords of this region are frustrated that Magadha has had too much dominance in the East. He immediately allies with these kingdoms and annexes them into the empire.
Alexander, now having access to the war elephants and vast armies of the West, invades Magadha and after a long and costly war, succeeds in defeating the Nandas.
Alexander reaches a roadblock at Central India. The tribes and kingdoms of this region are fiercely independent and refuse to yield, so instead, he immediately begins to fund a vast navy to set off from India to explore what he believes is the Eastern Ocean. This navy manages to land at Sri Lanka, the Malay kingdoms, and Indonesia. Furthermore, Greek explorers in the Tarim Basin find a pass through the hostile terrain of the region: the Hexi Corridor.
Soon, Alexander learns from the locals of the Tarim Basin of a wealthy and powerful civilization across the corridor. He plans on following this corridor to reach this civilization. But first, he must defeat the Xiongnu tribes living north of the corridor. Alexander defeats the Xiongnu and the various Xiongnu tribes agree to submit to Alexander.
Finally, Alexander arrives at China in the Warring States period. He conquers the North China Plains, which leads to millions of Chinese fleeing to the states of Qin and Chu. Alexander invades these states as well, and manages to conquer them in a bloody war. Soon, his forces also invade and conquer Korea, modern day Southern China, and Japan.
Alexander then marches back to Babylon, where he decides to conquer the Germanic and Celtic tribes of Western Europe. After conquering modern day Germany and France, he invades the island of Britain as and also invades Southern Scandinavia, until he meets his greatest enemy yet: the winter of Scandinavia.
Alexander then invades Eastern Europe and reaches all the way into Russia, until again, the cold stops him. Then he continues back towards the Eurasian Steppes and subjugates the remaining Scythian tribes there.
Across the world, Alexander’s generals expand the empire. Ptolemy expands the African provinces, while Seleucus is campaigning in East Asia. Antigonus invades the rest of Arabia. Alexander meanwhile goes back to Britain to end a rebellion, and successfully does so. Alexander now controls most of Eurasia and North Africa. In this time line, he does leave a successor, his son Alexander. The new “Alexandrian Empire� manages to rule Eurasia until various rebellions in the 3rd century AD end with it falling apart. Greek culture is also prevalent in areas like India, China, Western Europe, and Southeast Asia.
In the end, Alexander’s Empire looks like this.
It looks like what would happen if the Mongols, Romans, Guptas, Malays, Vikings, Arabs, and Swahili decided to merge their land together.
Also, I realize this is improbable. There is no effing way all this land could be controlled by one man. The Mongols couldn’t control an Empire about half the size of this one. They had to split it into four. Also please do not rant in the comments about how your country was strong and would resist Alexander. Again, this is an improbable scenario that was made just for fun.