Gaius Julius Caesar intended to invade the Parthian Empire to avenge the fellow triumvir Marcus Licinius Crassus, who lost the Battle of Carrhae along with Roman military standards (later retrieved via diplomacy by Augustus). However, Caesar's plans were obviously cut short when he was stabbed to death in a senatorial conspiracy against him and his veiled tyranny over the Roman Republic. Despite his unlawful usurpation of Republican powers and authority, even Caesar's critics such as Cicero found admirable qualities in him. Aside from his brilliantly persuasive rhetorical and writing abilities, Caesar was obviously the greatest commander of his day. His military career stretched from what is now Spain, to France, England, Italy, Greece, Egypt, Turkey, and Tunisia. The man was a prolific victor in battle and defeated Pharnaces II of Pontus at Zela so swiftly that he felt compelled to write a terse message back to Rome: "Veni, vidi, vici" (I came, I saw, I conquered).
Now, imagine the same man invading the Parthian Empire. Caesar was far too competent to repeat the logistical mistakes of Crassus and far too wily to fall into an obvious trap set by the Parthians or their allies. Even if he was betrayed by an Armenian ally, much how Mark Antony would discover years later, I can imagine Caesar somehow getting himself out of a bind and then winning the battle instead of retreating. He was, after all, the same guy who won at Alesia against the Gauls by ingeniously building a double set of walls around the oppidum hilltop town: one wall to keep the besieged in, and another to keep the Gaulish relief force at bay! This was hardly the only battle he won without superior numbers as well. He also knew how to entrench himself and hold out for the long run, such as when he and Cleopatra were trapped inside the palace of Alexandria by the forces of the Cleo's brother and Ptolemaic Egyptian pharaoh Ptolemy XIII (reinforcements didn't arrive until the early spring of the following year). He was also a master of psychological warfare, building bridges across the Rhine in short order, both to impress and frighten his Germanic enemies camped on the other side.
I'd venture to say that at the very least Caesar would anticipate the exploits of Trajan by snatching the major cities along the Tigris and Euphrates rivers, reaching the Persian Gulf. Perhaps he wouldn't have the manpower or logistics to repeat the exploits of Alexander the Great in invading Persia proper, but I could definitely see him taking Mesopotamia, perhaps on a far more permanent basis than later Romans emperors, whose control over it was ephemeral and virtually lasting no more than a year or so. Armenia would be quelled by later Roman rulers, and for that matter its king was even captured by Mark Antony a few years before he lost at Actium against Octavian. If Antony could do it, Caesar (being who he was) hypothetically could have conquered Armenia within a significantly shorter span of time.
What say you?