Plausible or not?

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?
 
First questions which comes to my mind:

How large a border troup would he need to defend the East while he is busy in the West?
Can he feed the army on the march through his own empire to the West?
And which ratio of his army will be left (from diseases and desertion) when he can start?

I think the point is that one cannot just move armies around like counters;
but as I don't know the answer to the above questions, it might be possible ...
 
He did, if I recall; he wrote it in a history book of his, as a chapter asking the WI question.
 
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