Can Alexander the Great, having conquered the Persian Empire, go West instead of East to take Carthage, Sicily and Italy (Rome restricted to Central Italy at this point), then South for Kush and finally East to the Indus (possibly with breaks). His Empire is larger, but does he live for longer allowing his son Alexander IV of Macedon to grow up enough that the Empire has a strong central figure when Alexander the Great dies? Does this allow for the greater part of the empire (say Greece, Mesopotamia, Egypt and Persia) to remain intact and the dominant player of the region, or will the Empire fragment just as spectacularly?
As a rough timeline, I'm thinking:
332-318 BC-Campaigns in the Western Med.
317BC- Campaign in Kush
315-310BC- Capaigns to the Indus.
Alexander dies with 1 son in late teens, early 20s, and perhaps a few more children.
So, does the Empire survive?