Causes and effects of a stronger and a more influential Graeco-Bactrian/Indo-Greek Empire

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Graeco-Bactrian kingdom, later becoming the Indo-Greek Kingdom was a Hellenistic kingdom in today's Afghanistan, Iran, Pakistan and India formed after the conquests of Alexander the Great. It was an influential kingdom and adopted Buddhism as a Hybrid with the Greek religion.

In an alternate scenario, you need to get a larger and a more influential Greek Hellenistic kingdom in the region with a thriving Greek populace, Hellenized immigrants, a stable economy and a larger territory and in regular contact with the Greece/Rome in Europe. Find the realistic scenarios possible for this.

How would you decide the effects of this larger empire on Persia, West Asia, Rome(Europe) and India?
 
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