Alexander the Great

[Cataphract_Of_The_City]

Keep in mind that if Alexander decided to go on instead of turning back, he had a force of 300 trained war elephants (which he would use in their utmost efficiency and in innovative ways), a large, battle hardened and superbly drilled army and he was the richest king in the world, with the resources of millions upon millions of people from Greece to Bactria. He had faced one Indian army and he was quite adept at learning from his mistakes. Huge numbers he had faced and in locations where they could be used in outmost efficiency. India is not exactly the place where huge numbers can operate with impunity. As such, I can't see any single reason on why wouldn't Alexander be capable of conquering the whole of India.

[Rosacrux redux]

But Alexander wouldn't be able to move on eastwards - it was not his decision to back off, it was the will of his veteran soldiers. He alone couldn't do much now, could he?

Alexander was a victim of the Greek culture, in that account. Had he had an army of easteners, they would march with him to the end of the world and beyond. But with the strong-minded, individualist Greeks... well, after so many years of campaigning they just wouldn't take it any more.

As to the "what if" side of the argument... I think he could effectively play a different game here - divide and conquer. I tend to think of him as a rather innovative statesman ...I believe a pupil of Aristotle, commanding the vast resources of the Graeco-Persian empire, would be absolutely capable of playing one against the other the Indian hegemons, ally with one to take out the other... What the Romans did in the eastern mediteranea, just in a reduced timeframe. I don't think it would be easy to take and hold by solely brute force India, but he knew his trade well and was an exceptional military leader.

[Kraxis]

If we assume that the homegrown troops had not opted to resist Alexander, then I believe there would have been a series of battles in rapid succession. Alexander, having learned from his experience against Porus would have become better and better against the Indian armies.
But eventually he would realize that India was not really worth it. Unpleasant and far between riches (oh yes there were riches). He would sign agreements similar to protectorates and then head off to fight the Chinese instead.

[Rosacrux redux]

...and the next question arises: what would he do against the Chinese?