I mean, Alexander eventually did push those borders farther to the East, admittedly, a less impressive feat since Persia had by this time fallen into a dozen different warring factions. Never reached India though, given he had to head back West to deal with the Gauls invading Italia. God did he make them pay for making him have to stop short of the Indus.
Let's be real here: Alexander was never in sight of the Indos. After he succeeded his old man, the Akhaimenids were overthrown for losing all that land, and some factions in the succession struggle were planning renewed war. Alexander led has army into the Persian heartland, struck a deal with the most powerful Parthian war-host, and cleverly re-directed
their efforts towards the Indos. (After all, the already-declining Nanda empire was in turmoil after Chandragupta's attempted coup.)
Persia was left as a collection of more-or-less unthreatening states, and Alexander went back home before his very presence could unite them against him.
Of course, then he led that campaign against the Gauls, which was a whole big waste of resources and got him nothing he really wanted to keep. He's lucky his son was a good administrator, or the Empire would have fallen mere decades after Philippos forged it together. Alexander's son, Argaios, wisely withdrew from most of Spania and from Gaul proper. would've been an endless quagmire to stay there.
...my point is: holding all of Persia would've been much the same. You either "go native" and lose greece proper after some time, or you try to impose Greek rule and you get overthrown before long. I do agree with you, then, that you'd get a "Macedonian" Empire that would be Persian... because it would probably be a Persian Empire with a Macedonian dynasty, which no longer even includes Macedon itself! My bet is that Alexander would just head East, establish his capital in Persepolis, and rule from there.
Might he have continued trekking east and taken India?
I really doubt it. That's just a story based on myth-making in OTL. as I said: alexander only ever sent the Parthians off towards the Indos in a clever geo-political move that caused the Indo-Parthian Contention.
That kept all parties occupied, and that allowed Argaios to consolidate the Macedonian Empire in the decades afterward. If Alexander had taken Persia completely, that would have surely satisfied him? Persepolis would be he biggest prize of all. What do you imagine him doing? Burn it all down and keep marching East? "
Wow, nice golden throne, but no thanks, I prefer ten more years of campaigning"? Don't make me laugh. Nobody would be that stupid.
The way I see it, if Philippos dies, Alexander carries out the big plan, but doesn't make a deal. He conquers all of Persia (or dies trying, but let's assume he makes it), and then he has to actually pacify it. That would surely take a while, right? He'll never have a chance to even consider going further east. At most, he'll see Chandragupta's coup (if it happens here) as a cool opportunity to keep the enemy busy. Maybe he'll fund Chandragupta, so that the coup doesn't fail in this ATL, and he'll have a loyal vassal/friend beyond the Indos. t's not like Chandragupta could be a threat anyway. Look at what happened to the Nanda Empire after he was executed in OTL: it just fell apart. No danger there at all.