You will be undoubtedly disappointed, that the historical paper trail for any empire is extremely scanty. There was no Roman, "Great Map of Our Projected Territories".

The great trail of dinner conversations, scrawled drawings, quickly written notes, and newspaper scraps that comprise statecraft today meant that Roman conquest was not like, "We are the Great and Mighty Romans, masters of the world, thus we must wrest from the hand of the ignominous Persian the province of Iraq".

Usually something more like, "I, Romulus Unnotableus, governor of nowhere in particular, I've decided it's better to let that fool Flavius Whateverius lead his silly campaign into Armenia after all, because if he fails it will certainly make Julius Arselickerus look better, and I need his good word with the Emperor to get funding to improve my crappy aqueduct".

Generally speaking, it's a fools errand trying to map simplistic motivations like, "best Alexander" to ancient figures. I hardly see why the conquests of some Greek notable living nearly 900 years before Heraclius would inform his plans. Do you dream of conquering England like William? Any effort to conquer Iran would be insanely expensive, at no real practical benefit to the Romans. As far as they were concerned, they ruled the whole civilized world anyway. Any design on Persia by any Roman general or basileus would almost certainly be fleeting and temporary, very much seizing the moment, which was often too short to capitalize on anyway.