So we know that until the 1st century BC, some form of Greek kingdom (Bactria or Indo-Greeks) existed east of Persia. What if Rome, to attack the Parthians from both sides, decides to ally the Indian Greeks. They have more in common culturally than the Romans or the Greeks with Parthia or India. They can understand themselves mutually, as the Roman ruling class speeks Greek. They can communicate through sea travel, since Rome can use the ports of allied/puppet Egypt to trade with India and Bactria.
It's quite clear that this alliance wouldn't be between equal partners, since the Indian Greeks are on the brink to be conquered by neighboring tribes, whereas the Romans haven't yet arrived at the climax of their power. Though, the Romans could help the Bactrians by sending money (gold) and instructors, so that the Bactrians can build up an army similar to the Roman legions.