The Roman Empire had extended beyond the Euphrates since the second century CE.
The Roman province of Mesopotamia had been established by the Emperor Septimius Severus in c 198 CE. (Technically, one might argue that the province was re-established by Septimius Severus, since an earlier province had been established by Trajan, before being given up by his successor, the emperor Hadrian).
In 250 CE, Shapur I of the Sasanian Empire invaded Mesopotamia. He fought a series of wars with the Roman emperor Valerian (r. 253–260), who he eventually captured at the Battle of Edessa in 260 CE.
However, the following year, Shapur I suffered a massive defeat at the hands of Odaenathus of Palmyra and his forces were driven out of Mesopotamia.
When Odaenathus' son Vaballathus established the short-lived Palmyrene Empire in 270 (under the regency of his mother, Zenobia), it consisted of most of the eastern Roman provinces, including the (by then reduced from its maximum extent) province of Mesopotamia - and so it did indeed extend beyond the Euphrates.