How much Alexander can realistically conquer if he would live longer? On some point there would be several rebels and probably some plots against him by his own military leadership. Rome probably was on this point too weak resist Alexander's conquest.
Fact is, he had just solved most internal restistance, and he was actually rather popular with the general populace. If Alexander lives, mass revolts aren't that likely, and besides Kassandros, enemies in his own ranks have been dealt with. It's his demise that's the big threat.
If he lives longer, he can realistically take Arabia and North Africa for sure. Trouble had been brewing in northern Anatolia (parts of which were not under his control), so i can see him mounting an expedition there, pushing the northern border of his empire to the Caucasus. The Samnites in Italy had killed his uncle (Alexandros the Molossian), and revenge was in the cards. Considering that, an alliance with Rome is more likely than a fight with Rome. Alexander might be inclined to annex the Greek cities in southern Italy to his empire, and then divide the lands between there and Rome between himself and the Romans.
Potential other steps, though less likely, include annexing Greek cities in the far west, such as Massalia, and launching an expedition to annex the Crimea and the western coast of the Black Sea (which also had Greek settlements). All this in light of a desire to unite all Greeks under his aegis. Finally, I can see an expedition against the Illyrians happening.
A second expedition to conquer India would remain a fond wish of Alexander, but I don't see it happening. By the time he'd be ready to give it a second try, Chandragupta Maurya would already have taken control there. So let's consider: Indian armies were vast, the terrain was largely unfamiliar to Alexander's troops, fighting enemies who have elephants is not fun, and Chandragupta is an extremely capable leader himself. On those grounds, I feel confident in writing off a second Indian expedition. If Alexander tries it, it'll be his doom.
