They did...it's all over the sources...

The Parthians crossed the Euphrates only twice. In 51 Cicero feared a Parthian invasion into Cilicia, but it did not materialize, and the brief Parthian campaign following Crassus' defeat fizzled out quickly. Plutarch claims that Pompey reached out to the Parthians for asylum, but he ended up going to Egypt instead and the Parthians were not active on the Roman frontier for most of the 40s. A Parthian campaign in 41, led by the younger Labienus, was initially successful, but they were disastrously defeated by Ventidius Bassus, losing the crown prince Pacorus. The Caesarians' success at Philippi allowed Antony to launch a large expedition into Armenia, which was not particularly successful but was not followed by a Parthian counterattack. Though wars were occasionally fought in Armenia, and the Romans successfully invaded Parthia a few times (under Trajan and Septimius Severus, for example), the Parthians did not again cross the Euphrates.