I have to question the inclusion and relative accessibility of Tibet, given that afaik no Indian or Central Asian empire has ever successfully launched an invasion across the Himalayas. Every attempt that has ever been made was a complete disaster, and all occurred well outside the classical era. Trade is one thing, but trying to send an army across the Himalayas into Tibet is frankly suicide, and few leaders have ever been stupid enough to try. The Tibetans themselves did at have a bit more success going the other way, but that didn’t happen till the 7-8th centuries, well outside Imperator’s time-frame.
We don't know how hard it will be to cross passes with a large army.