If the Republic was moldering in its grave by 41 AD, the corpse had long since been reduced to nothing by 180 AD.
While Marcus Aurelius could have been an idealistic dreamer who fantasized about restoring the Republic (although there’s little evidence of that), there is no way it could possibly have accomplished, any more than Barack Obama could plausibly expect the United States to revert to the Articles of Confederation.
So the idea that a serious conspiracy could be hatched to accomplish this pipe dream is pretty silly.
It becomes slightly more plausible if we assume that Gracchus or Gaius is hoping to make himself emperor by using Maximus to depose Commodus and then get rid of Maximus, but there’s no evidence that that’s what they’re up to.
He feels that Maximus has the moral qualities that will enable him to accomplish this feat, while Commodus lacks those virtues, and thus Marcus makes the choice to declare Maximus his successor, although Commodus murders him before he can announce the decision.
Thus the film’s plot is driven by Marcus’ idea of restoring the Republic. Senator Gracchus (Derek Jacobi) and Senator Gaius (John Shrapnel) both want to see Rome returned to a Republic as well.
Furthermore, the collapse of the Republic was due in considerable measure to forces unleashed by the expansion of the Roman state outside the Italian peninsula.
The Republic was essentially a system set up to run a single city; the Senate was in many ways like a large city council.
They plot with Maximus and with Commodus’ sister Lucilla (Connie Nielsen) to foment a rebellion that will overthrow Commodus and put Maximus in control, so that he can empower the Senate to rule Rome again. The Roman Republic, which was founded around the year 510 BC (at least according to Roman tradition), entered its decline in the late 2 century BC.
So while the memorable part of the film is the conflict between Commodus and Maximus, the actual plot of the film is an attempt to end the entire system of the Principate (as modern scholars term the rule of the emperors in this period) and re-establish the system of the Republic. This period, termed the Late Republic, is generally taken to have begun with the disputed election of 133 BC, during which the supporters of the populist tribune Tiberius Gracchus (note his (high priest), rioted and massacred Tiberius and around 300 of his supporters in the street.