Some did. Pharnaces II of the Borporan Kingdom invaded Roman territory in the middle of Caesar's Civil War to try and reconquer Pontus. (Pontus had been ruled by Pharnaces's father, Mithridates the Great, but had been conquered by Rome during the Third Mithridatic War.) Pharnaces had some initial success in his campaign but then Caesar came north and stomped him at the Battle of Zela in 47 BC. (The battle that inspired the "veni, vidi, vici" quote.)

Likewise the Parthian Empire allied with Quintus Labienus (the son of Titus Labienus who was one of the main generals opposing Caesar during his civil war) and invaded Roman controlled territory in 40 BC, with the Parthians overrunning Syria and Judaea, and Labienus pushing into Asia Minor before the Romans counterattacked and drove them back. The Parthian invasion occurred around the same time as the Perusine War (a civil war fought in Italy between Octavian and Lucius Antonius (Marc Antony's brother) and Fulvia (Mark Antony's wife) and benefited greatly from the Romans being distracted. (Mark Antony should have been leading the defense of the eastern provinces but he instead went to Italy to confront Octavian.) It was only after Antony and Octavian came to a new accord and Antony sent his best general, Publius Ventidius, along with several legions back east, that the Romans were able to kill Labienus and drive the Parthians out of Roman territory.

And the Parthians struck again during Antony and Octavian's final civil war when they took advantage of the Romans being distracted to invade the Roman client-state in Armenia and the Roman allied kingdom of Media Atropatene and install Parthian friendly governments.