Ayup, Kory, the other posters have the right of it. It'd be a huge stretch to negotiate Alexander onto the Ganges, relying on massive luck and multiple PODs to sufficiently disrupt and weaken India.
He's just not bringing an army to China, much less Japan. If you want him there, have him never get to India. The India, Indochina, China route is just too long and too hostile. If the Persians are wilier, though....
A group of local governors see the writing on the wall early on and get organized. We'd better assume they're members of the same family - otherwise a conspiracy of that scale'd never happen. Each ostentatiously revolts against the Persians just before Alexander arrives, and work to ingratiate themselves with the conquering Greeks. They eventually stumble across generals and soldiers from Polis' like Athens that resent Macedonian dominance.
Just as Alexander's army is fighting a battle in Afghanistan, revolt breaks out behind him. The the family cut a series of deals with Greek generals in the rear for marriages, governorship of provinces, and support of the Greek revolt. There were certainly enough plots against him historically; with the right organization and some luck they could probably be successful. Along with some Greek forces left in the west, the newly-trained Persian hoplites are coopted. Alexander overreacts to the threat of dissention in the ranks and purges his army of suspect individuals, hurting morale and fighting strength. On the other hand, what remains are his most rabid loyalists....
When Alexander and the rebels fight a major battle near OTL Tehran, Alexander suffers his first great defeat. He makes a fighting retreat across Bactria, gathering what local support he can before suffering a final defeat at the extremity of the Persian Empire in Central Asia. During the battle Alexander and a remnant of his army fight their way out of a potential encirclement. Night falls with the effort clearly lost, but Alexander still alive. The man expected a glorious death or triumphant victory, and finding himself with a third result, he spends the night thinking. He could turn back and simply choose death - charging into the armies of the victorious Persians, but he's used to having the possibility of victory when he does something stupid....
A new day dawns and the Persians discover Alexander has taken his remaining 8,000 men and marched out of the empire. Rather than trying to live off the slim pickings of Central Asia, Alexander's men quickly turn to the one source of wealth to be found: A year later they are alternately looting and serving as mercenaries along the length of the Silk Road.
By the time of Alexander's OTL death, they have acclimatized to new forms of warfare. In the process they have "allied with" (more like absorbed) a couple local Tocharian horse-tribes. The situation is unsustainable however. Too many long marches between sources of water and food are required, and often Alexander must split his forces temporarily just to keep them alive. Their reputation attracts the attention of the Qin, the westernmost "Chinese" state. So when an offer comes for better employment, the Greeks march east once more....
Alexander spends a decade switching sides between the warring states of China. In the process he maintains his numbers by recruiting from the Han and from the horse nomads (Tocharian and proto-Mongol) of the north and west frontiers.
Finally, a now middle-aged Alexander decides to settle down. With most of Alexander's soldiers married or with families (including a lot of polygamy), the "army" has gradually transformed into a volkswanderung of nearly 40,000 that refers to itself as The People more than The Greeks. The Han states outnumber him and are increasingly adapting to Greek military tactics, so conquering there is unfeasible. To the south are potential targets, but he and his Greek veterans pine for Macedon's climate. The migrate to Korea, "paying" the intervening Chinese states by not looting them to much in passing. The first local kingdom of Korea - Gojoseon - had long been declining in the face of local feudatories, and Alexander's heterogenous people are able to conquer them piecemeal.
Having seen the wages of half-measures in Persia, the conquest of Korea is probably an ugly thing. Military-age men are wiped out entirely. In the portions of Korea where the people actively settle, this is extended to include all males. The result, naturally, is that the light-skinned, light-eyed, and sometimes light-haired core of the conquerors immediately breed themselves out of existence. Only a small minority of the next generation is light-haired, and these are mostly Tocharian speakers, but the skin tone and eye color of Korea begin a permanent change. While Greek survives, it's massively altered by substrates from Han Chinese, Tocharian dialects, and especially proto-Korean. Parallel Greek, Tocharian, and Korean religions exist for a time, but eventually the former two merge, while the latter is subverted as a "lower pantheon". In practice, the day-to-day Korean folk traditions come to dominate.
At the age of 66, after 20 years in his new kingdom, Alexander goes on his last campaign. Responding to raids from Japanese raiders ongoing since Alexander's invasion first disrupted Korea, he's led a series of invasions of Japan. Mostly - as the saying goes - they burn, butcher, and bugger off. This last, though, attempts to resolve the problem by subduing all of Kyushu and maintaining a fortress there to keep the tribes under threat.
When Alexander returns to his capital at Alexandria (OTL Pyongyang) he finds things beginning to change. Shown the way by Alexander, a series of Tocharian invasions of the western Han states has begun. Some, less interested in loot than in land, migrate all the way to Meizon Makedon and settle alongside the conquering class. They bring news from distant Persia, which has absorbed Greece and is losing a long war in Sicily against people's unknown. Interested, and distrustful of any conquered people, Alexander encourages further migration by awarding land to the newcomers. Meanwhile, the third generation of the conquerors in Korea is being born, and showing the surprising tendency to have colored hair and more color to their eyes. [Aside: As a recessive trait it would disappear right off. It returns because all the people with it are going to have massive reproductive success, and their children will tend to intermarry.] At court such flukes of appearance are solidifying as a mark of status, and duels are fought over the untoward success the offspring of Tocharian families have with women.
Alexander dies of a cold contracted at sea enroute to his new empire.
