Why would Crassus's conquest of Mesopotamia be more provocative of a war than, say, Caesar's conquest of Gaul?
If Crassus (or his son) conquers Mesopotamia, that means they're still alive and the First Triumvirate will last a bit longer than OTL. IIRC it was the death of Crassus that destabilized things and paved the way for the civil war.
Because the conquest of Mesopotamia could bring Crassus to control the wealthiest and prestigious cities of Babylon, Ctesiphon, Seleucia, the trade routes to the East, he could give the possibility to create here new clienteles making him more rich and powerful and also the possibility to finally have his first triumph at Rome demostrating to be a valiant general (remember the Senate gave only an
Ovatio for ending Sparthacus's revolt, so for Crassus was surely a sweet revenge). The civilized Mesopotamia is many times more valuable to a barbaric Gallia in the Senate's eyes.
A problem for Crassus is the territories he now controlled (Syria, Iudea, Mesopotamia) were surrounded by Pompey's client states ( Egypt, Israel, minor Anatolians ); also in Syria surely Pompey continued to have support.
So Crassus could try to impose his influence in these regions or he waited until 48 bc ?
In effect if Crassus survived at start of 48 bc his power as Proconsul in the area ended as for Caesar in Gallia... so the debats in Rome surely become more complicated than in history... and the only possible options were or a new triumvirate accord or the civil war: but for Pompey the situation were disastrous...
Maybe, with the East provinces in hand to Crassus instead to flee in Greece Pompey could try to resist in Spain?