Yeah, Alexander was made to turn around when attempting to invade India, and was planning on attacking the coastal kingdoms of the Arabian peninsula when he died. He might have considered the Greek colonies in the Mediterrenean his allies in spirit if not in arms (we're talking Greek colonies in Spain, France, Sicily and Italy now), but the fledgling Roman alliance and above all Carthage was out of his grasp (although Rome was mostly irrelevant at this time).

The Greeks considered the Carthaganians offshoots of the Phoenicians of the Levant, and fighting between Syracusae (a Greek colony) and Carthage in Sicily during the time of the Persian invasion of Greece that would culminate in the Battle of Salamis was interpreted as an alliance between Carthage and Persia by the Greeks (there's little to no evidence of such an alliance outside Greek sources, and the general consensus among scholars today is that there were no such alliance).

What Alexander did was to conquer the greatest Empire of the known world. India was largely unknown at the time, the proto-Arab states were small fish on the international scene, Rome was nowhere near its later size and power.

Once could say that Alexander had conquered all relevant parts of the known world (except Carthage) and had allegiance from all Greeks (except the Spartans).

Europe beyond the Greek, Aechemenid and Carthaganian world was filled with barbarian tribes that offered little but potential slaves to a would-be conqueror. China and India was mostly unknown then.

That statement is a bit of a fallacy and it has fallen out of favour in recent years. It stems from the heavily eurocentric idea that the classical world was an isolated font of civilization surrounded by savage barbarians.

/u/vonadler already covered it very well but I just want to reiterate certain parts of what he said. Instead of the 'known world' it is more accurate to say the 'rich and relevant parts of the world'. This is a bit of a generalisation, but the Greeks were aware of the fact that there were many unexplored places and cultures in the world, but most simply didn't care. Why bother with conquering a small nomadic tribe in an empty steppe when an empire with the richest cities known to you could be yours?