It's not surprising that this is a popular subject, given Ptolemy's famous scenario in his History of Alexander, where he contemplates Alexander going east, and concludes that Alexander would likely have conquered the whole Empire. I know a lot of determinists brush this scenario off as unrealistic at best and laughably ASB at worst, but a deeper look makes such a view less clear. Ptolemy's scenario really doesn't help, because it is riddled with historical inaccuracies and anti-Persian bias, but we shouldn't risk swinging to the other extreme and automatically and unilaterally dismiss such a scenario as ASB. Assuming Alexander decides to invade the Persian Empire, he actually has quite a few factors on his side. First are his own advantages: he has a highly trained and organized army that is definitely superior to the Achaemenid forces, he himself (assuming he and his generals are as good as OTL's) proved themselves to be great tacticians (most of the time), and he proved to be personally lucky in battle and willing to risk his life to lead charges. Even greater were the advantages of timing: his ascension to the throne coincided with dynastic turmoil within the Persian Empire, with the poisoning of two Emperors by Bagoas before Darius III forced Bagoas to take his own medicine (read: poison), and the fact that many Satraps and notables in the Empire were quite discontented with Persian rule. Another longer-term factor was that the Persian treasury was draining silver from the provinces that would never again be circulated throughout the Empire. This lead to troubles even for Satraps and landlords who could not come up with the hard currency to pay loans or debts, which only furthered discontent with Persian rule. A final factor that cannot be ignored was the Empire's increasing inability to hold down the western portion of its Empire. Egypt, for example, remained independent for a surprisingly long time, only subdued shortly before Alexander ascended to the throne. Asia Minor was effectively a demilitarized zone between Athens and Persia. I don't think a lot of people recognized how precarious the situation in the Persian Empire was at the time, or how well Darius III did even to keep his throne and Empire relatively intact. I would conclude from these factors that a lot actually depends on the nature of Alexander himself, and how lucky he gets. If Alexander retains an energetic "conquer the world" attitude as he had in his early years IOTL, he might've gone for the whole cake. If he had tired of conquest part of the way through, he might've been content in carving the western part of the Empire out for himself, leaving the East to its own devices. But from the Empire, he would inherit a slew of his own administrative and cultural problems that would hamper him and his successors. If even the conquest of Karchidona, Megas Hellas, and the Tyrrhenoi caused internal frictions and rebellions, then I can only imagine the cultural disruption that the entry of Hellenistic culture into the East would have.
As for Karchidona and the Tyrrhenoi, they could go in many different directions. I'd say that they'd likely remain regional powers, but anything is possible.
Anyways, this scenario's probably pretty unlikely. It would be so easy for Alexander to lose a battle, or die, or burn out, etc. I'm just saying that Ptolemy's scenario isn't totally ASB, it just needs some reworking to become plausible, even if unlikely.