Historians mention some of his plans. In short, he would march south and west and try to mix the population of his empire. As for the long version:
Before his death, he had prepared for a large-scale invasion and colonization of Arabia. As Arian said:
Near Babylon, he dug a port large enough to berth 1,000 warships; adjacent to the port, he built a shipyard. Miccalus the Clazomenian was sent to Phoenicia and Syria, with 500 men to recruit some and buy others with sailing experience. Alexander aimed to colonize the coastal areas near the Persian Gulf and the islands in the sea. For he thought that the land would become no less prosperous than Phoenicia. He used the excuse that the Arabs were the only barbarians in the region who had not sent embassies or done anything else to make their position and pay homage to him, preparing the fleet for the main body of the Arabs to attack. But the truth is that, in my opinion, Alexander's ambition to acquire new territory was insatiable.
In fact, Arian mentions that the army is already there and the navy is training, which means that they are about to launch this battle.
When he returned to Babylon, he found that the Peucestas had arrived from Persis, bringing with them 20,000 Persians, as well as many Cossaeans and Tapurians, as these races were reportedly the most belligerent of the races bordering Persis. Philoxenus also came to him and brought an army from Caria. Minand and another man from Lydia, as well as Menidas and the cavalry he commanded. （...... At this time Alexander often looked back on his fleet, engaging in several false battles with his three-column battleships.[2]
[3] After the Battle of Arabia, his plans were mentioned a few lines later, in a letter to the Egyptian commander:
"If I find out," the letter said, "the temple and chapel of the Egyptian hero Heffistion have been completed, and I will not only forgive you for any crimes you have committed in the past, but you will not suffer any unpleasant treatment in the future."
Where will he go after Egypt? Diodorus Sicelus describes how Klatrus built a large fleet in the Levant on Alexander's orders to carry out operations in the Mediterranean, and went on to describe his other plans.
The construction of a thousand warships larger than the three lemas in Phoenicia, Syria, Silesia and Cyprus against the Carthaginians and others who inhabited the coasts of Libya and Iberia and up to the adjacent coastal areas of Sicily; along the road between the Libyan coast and Hercules, and in the right places according to the needs of such a large-scale expedition; the construction of six of the most expensive temples, each costing fifteen million he had; and finally, the establishment of the city, The migration of populations from Asia to Europe and from Europe to Asia in the opposite direction in order to enable the largest continents to achieve common solidarity and friendly kinship through intermarriage and family relations. The temples mentioned above will be built in Delos, Delphi and Dodona, in Macedonia, in the Temple of Zeus in Dium, in Amphipolis the Temple of Artemis Tauropolos and in Sernus. Build a temple that no one can surpass. The tomb of his father, Phillips, will match the largest pyramid
So, more Alexander, but in Africa and Europe. Arian summarizes the hypothesis about Alexander's further campaign in the following paragraphs:
Some authors have also stated that he was meditating around much of Arabia, Ethiopia, Libya and Numidia, crossing the Atlas Mountains to Cadilla (Cadiz), and inward into our sea (the Mediterranean), thinking that after his conquest of Libya and Carthage (Carthage), he might be called the king of all Asia. Because he said that the kings of the Persians and the Medes had no right to call themselves great kings because they did not rule most of Asia. Some say he was meditating from there sailing to the Eusin Sea, to Scythia and Lake Meotis (Azov); while others asserted that he intended to go to Sicily and Cape Ibbia, because the fame of the Romans had spread so far, now aroused his jealousy. Personally, I can't speculate with certainty what his plans were. I don't care about guesswork either. But I think I can be confident that he has no small things or despicable meditations; and that he will never be satisfied with any acquisition he has made, even if he adds Europe to Asia, or the British Isles to Europe; but will continue to search for unknown lands.
Thus, Alexander would fight around Arabia, then through Egypt to Libya and Carthage to Iber, and then to Sicily. He would also mix people together to unite them, as he did in Asia, and also built many buildings, mainly temples.