So there was the emperor Julian for one...

Julian is an interesting case. He was the nephew of Constantine the Great, you know, the guy who did more than anyone to move Christianity into the halls of Roman power. Julian however was not so endeared to the new religion of the empire. He grew up Christian, but following his education in the Greek speaking East of the empire, he embraced a more esoteric version of the Hellenistic religion that we know and love. (There's a lot of complicated theology and philosophy behind this distinction and its not really worth delving into in detail, suffice it to say he was a pagan but not really the exact same as a previous Roman pagan emperor liek Augustus)

Julian attempted to overhaul the Roman state and its relationship with both Christianity and Paganism, but also bureaucracy, education, economic subsidies and much more. Julian had ambitions to overturn the Roman state from the form that he had inherited into a more streamlined, and militarized, state. Now how much of this was ever actually going to pan out is rather uncertain, because Julian died after scarcely two years in the purple. But we do have an idea of the steps that he took to try and revive paganism in the empire.

These included:

Re-opening pagan temples that had been closed

Re-distributing lands that had been seized from pagan temples and landowners

Cutting the subsidies and stipends that the Roman state had paid out to Christian officials, both Church figures as well as educators and institutions that were Christian

Restricting the teaching ability of Christians and banning them from engaging with Classical Pagan texts

Attempting to revitalize pagan practices by inculcating new approaches to public worship and the public practice of paganism.

These various efforts were.... mixed in their actual results. Julian enjoyed a great deal of personal popularity during his brief reign, and was able to enact much of what he wanted to. The tricky question is how much impact this could have had in the brief time that he was on the throne. Christianity had started to become deeply ingrained into the empire, and his efforts were very much swimming against the tide of religious change. Combined with his short reign this was not a recipe for success, despite his own personal popularity in much of the empire and with the army. His attempts to reform the bureaucracy, Roman religion, and so much more did not outlive him.