He had already fulfilled his goal (?) of conquering the Persian Empire, so what drove him to go looking for even more conquests when his empire was already arguably unmanageable?
Alexander had this vision of reaching the outer ocean. In other words "the end of the world" in his mind, though I don't think he realized it would be so far. The only reason he stopped was because his men refused to go any further. Furthermore he wanted to conquer as much as he possibly could, not just the Persian Empire. I believe it is referenced in Arrian, I don't have my copy handy but Arrian says he also had ambitions to conquer the Arabian Peninsula and west of Greece, Italy, Iberia, the northern tribes etc. It's plausible to say his "retreat" back to Babylon was really an intermission so he could raise the next generation of Macedonian and Persian soldiers to fulfill those ambitions.
Arrian notes that Alexander made plans to conquer Arabia, Carthage, and Europe, albeit after he was turned back from further excursion into India by his troops. The overall impression after reading Arrian and Plutarch is that his plan was world domination, initially sold as a justified counter-assault on the Persian empire.
Remember, Philip II had a seriously expansionist policy which Alexander was groomed to continue. Philip made inroads against the Illyrians, made marriage alliances with both the Illyrians and the Molossians, gained favor with Epirus, turned the Thracians into a dependency, and with Alexander as his right hand conquered most of Greece.
It must be noted that Alexander never really marched outside the boundaries of the Achaemenid empire. Even in India, he only crossed the Beas river once and when he did he didn't go more than a few miles into foreign territory. And he initially arrived in India by putting down revolts and securing his conquests. If the ancient sources are correct, he did intend to venture into India before his troops mutinied and the reason that is given is Alexander's obsession with glory, however I think that after nearly a decade of campaign where he had met hundreds of different tribes and traveled through dozens of distinct regions he wanted to discover more and he just happened to possess an army that allowed him that.
Edit: Robin Lane Fox's "Alexander the Great" is an essential for anyone interested in Alexander
Irrational exuberance