Toynbee
British Historian Arnold J. Toynbee once wrote a Super-Alexander-Fiction.
In short:
323 B.C.
Alexander is cured from his almost-deadly illness. He becomes a lot calmer
and lets his loyal officers Eumenes, Perdikkas and Ptolemaios rule the empire during his the next few years when he is campaining.
322 B.C.
Alexander sails around the Arabian peninsula, thereby discovering the Monsoon. In Suez, he orders the renewal of the channel of pharao Necho and king Dareios I.
As planned, Phoenicians are settled at the Persian Gulf, along with other neighbouring peoples as Samaritans, Moabits and Arameans, also the Hebrew. They use their opportunity and become an open-minded people. No religious strive and therefore no religious movements which spring off a humiliated Judaism. Thus: No christianity (according to Toynbee).
Alexander's new Capitol becomes Alexandria in Egypt.
321 B.C.
He sails to Macedonia and secures the frontiers in Thracia and Anatolia.
Romans are beaten by Samnites (realiter).
320/319 B.C.
Conquer of Sicily and Carthage. Both are reorganized in the same manner as the Corinthian league (the leagues of Utica and Syracuse).
In Gibraltar, he founds the city of Alexandreia Eschata Herakleia.
Pytheas of Massilia whom Alex met in Gades receives order to sail around Africa.
318 B.C.
Greek-Roman Pact against Samnites
317 B.C.
Victory over Samnium. Southern Italy ("Magna Graecia") is reorganized as the league of Naples. Rome may conquer whole Italy and - if possible - Gaul.
317-314 B.C.
With the Mediterrean Sea in his hands, he forms a new army with Oscian mercenaries and moves to India. He conquers the kingdom of Magadha, Seleukos will be ruling there.
At the Ganges river, Alexander mets a Phoenican fleet that discovered the way to India by sea.
From now on, Buddhist missionaries move deep into the empire. Buddhism tolerates any historic religion. In Hellas, Zenon and Epikur write essays on Buddhistic philosophy. World state and world religion are linked together from now on.
312/311 B.C.
Alexander moves to the Jaxartes river. Having heard of the Chinese wealth, he joins an uprising and conquers China. Antigonos Monophthalmos is made king of China (as kind of stateholder, of course).
308 B.C.
Nearch discovers the sea way from India to China. In the following centuries, Chinese population moves down the islands in the south, making Australia a Chinese continent.
287 B.C.
Alexander dies.
His successor Alex IV. civilizes his empire, reorganizes administration, builds up infrastructure etc. In Alexandria, he builds a university ("Museion" for philosophers, "Hephaisteion" for Technicians). Heron discovers the steam power, Aristarch the heliocentric idea. Erastothenes finds that Earth is kind of a ball.
about 220 B.C.
A young Carthaginian named Hannibal has read the stories of Atlantis and hopes to find it across the ocean. Guess what he finds - yeah, right. The new continent of Antipodia.
The rest of the world slowly joins the peaceful and benevolent empire.
About 1930 A.D.
A historian named Arnoldus Toynbeenus sits in Alexandria and imagines a world where Alexander died. He shudders by the mere thought of it and praises Alexander LXXXVI.