Alexander the Great conquered India, China, Arabia, Rome... and found America

[Frodo]

The most he could have done in his lifetime (as far as additional conquests) was add Arabia to his dominions -which was on his to-do list before he involuntarily revealed to the world that he was in fact a mortal.  Now if you want to debate whether his successors could extend the boundaries of the empire to include India and beyond (after a lengthy period of consolidation of his OTL + Arabia conquests), that's another matter entirely.