Partially correct, and partially wrong. The great patricians and senators will try to keep down a plebeian, but this is equally true of a fellow-patrician emerging as a dominant power.
But people could and did succeed in Rome: your point is an objection, not an insoluble problem.
I would point out that not getting assassinated - or coming up against a power bloc that can stop you - is a problem with all 'Become Emperor of Rome' scenarios: and it was solved by all emperors.
It boils down to politics. A strong point of the Joint-Stock plan is that you make a lot of people wealthy: a broad power base is a strong power base.
Consider this: many ancient and noble Patrician families are in a state best described as 'genteel poverty'. Give them enough of a share to regain a place in public life - but about the same, or slightly less, than the share you sell to merchants, so that these aristocrats cannot dominate the power base and - and you've got a very powerful influence in the senate.
The other place to secure influence is the Army. Families of successful (or influential) generals and mid-level commanders must get a share. At least one Legion, within reach of Rome, should start receiving mass-produced high-quality equipment ....Or mass-produced equipment as good as the standard issue, but at factory prices - much to the profit of the commanders and the procurator. (This is legal in Rome: cost-effective supply was properly incentivised).
"The Joachimsthaler Legion stands with Rationus' is a declaration that will put a stop to any drastic setback.
Incidentally, I wouldn't even start on trying to get the Praetorian Guard 'onside' - too obvious, certain to alarm the Emperor, and fatal.
Improving the water supply, temple donations, and economic mobility: that's a good route to popular support - and the 'Vox populi' was a matter of importance in Rome. Not that it was a democracy by that time, but the ruling classes took great care (and great expense) to maintain popularity. And there was a direct 'Will of the People' channel in Rome: the Tribunes.
Arguably, they are a point of failure: your public works, equalisation of wealth for plebeians, and temple donatuons would count in your favour - and should - but the Tribunes are a point of failure if your enemies seek influence there. Note, however, that the tribunes existed explicitly as a counterbalance to the great patricians and the emperor: that's the way you play against 'the people who are already on top'.
Finally, be sure that you and your supporters are liberal with donations to the Temples. And, indeed, to the causes and projects of the existing Emperor's supporters... Some of whom will be happy to be shareholders, discreetly, because they're not all rich - old families, again - and financial dependence on the Emperor is an uncomfortable thing.
In short, you'd play politics. But politics powered by an important invention of the modern age - Shareholders - with crude steam engines to prime that particular pump with money.
A recent discussion post has compared the difficulty of an AI destroying modern human civilization to that of a modern human taking over the Roman Empire, with the implication that it is impossible.
The analogy has a few problems: first, modern humans don't have much greater raw intelligence than the Romans, only a bit more knowledge and tools; an AI would have a genuine intelligence advantage. Second, a high-tech civilization like ours offers many more ways for a genius to cause chaos than existed in classical Rome: it's more plausible that you can throw a few existing technologies together to create a superweapon than that Ptolemy could have done likewise, and there's no ancient Roman equivalent to hacking a nuclear launch system.
But taking over ancient Rome might serve as an interesting upper bound on the difficulty of an AI taking over modern civilization. And it's a theme of Harry Potter and the Methods of Rationality that rationalists should be able to come up with creative solutions to seemingly hard problems. So if Professor Quirrell offered it as an extra credit assignment, how would you take over Rome?
Here are the rules:
- You are thrown back in time to the year 1 AD. You can choose to arrive anywhere in the world, but your method of arrival cannot itself give an advantage (you can't appear in a flash of light in the middle of a religious ritual or anything).
- You do not start with Roman citizenship or any other legal record of your existence.
- You keep your original physical characteristics, including sex, height, and fitness. You will appear in period-appropriate dress of your choosing, and can't carry any artifacts with you. You may start with enough money to live a patrician lifestyle for a year.
- You are intellectually near-perfect. You know all human knowledge as of 2012. You speak fluent Latin (and all other languages of the day) and can orate as eloquently as Cicero or Demosthenes. You are a tactical genius of the order of Caesar and Napoleon. And you have infinite willpower and goal-directedness: aside from human necessities like sleep or food, you need never rest.
- You win if you either become Roman Emperor (and are acknowledged as such by most Romans), or if a state you control conquers the city of Rome. You lose if you die, of old age or otherwise, before completing either goal.