There are two main PODs I can think of for this.
One is the one you allude to: that he decides to go on with a small cohort of volunteers after his army refuses to continue on. It's not very likely, because he was primarily set on conquering a vast empire. Exploring was part of it, but that was primarily related to a romantic notion of rivaling the mythic achievements of ancient gods and heroes. Alexander wanted to be Herakles and Dionysos combined. The conquering hero and the discoveror of the world's mysteries. He had this idea that the mythical mountain of Nysa (associated with Dionysos = "god of nysa"), said to be "in the East" was somewhere in northern India, and he'd very much like to reach it. But at the same time, he also expressed a goal of (at some point) conquering the west, reaching the Pillars of Herakles (i.e. Gibraltar) and thus rivaling that hero as well. When his troops refused to go on, Alexander chose (without much hesitation, once it was clear they really wouldn't go further east) to head back west, where he made future campaign plans (namely Arabia first, and then Carthage, which would allow him to reach the Pillars of Herakles-- needless to say, he died before that happened). It's generally believed that his conquest of arabia was meant to provide him with a springboard for a future invasion of India at a later time. (Having Arabia would make supplying his armies by sea much easier, after all). Given these factors, it is hard to imagine a scenario wherein Alexander opts to abandon his empire and go further into India as an explorer. Everything indicates he was planning to just go back west, and return to India as a conqueror later on. So while tempting, I'd suggest skipping that POD.
The other POD is much earlier. The reconciliation of Philippos II and Olympias never occurs, Alexander is never restored as heir, and he stays in Epeiros in exile with his mother and a small band of close friends. Philippos has another son, Alexander and Olympias become a clear threat, Philippos puts pressure on Epeiros to have them either sent to him as hostages or killed (or he invades outright)... end result is that Alexander has to flee for his life with his closest friends, pursued by his father's men, with no claim to his name. He ends up seeking refuge among his father's enemies: the Persians. In a great twist of irony, a surviving Pjilippos attempts to invade Persia... and is defeated by their mercenary general: his own son, Alexander. After this war, Persia is very secure, and Alexander becomes a great explorer, funded by the Akhaimenid dynasty (after all, this keeps him far away, ensduring he's no threat to
them).
Needless to say, this eventually gives us
A L E X A N D E R I N K O R E A