Well, first off, they'd have to take control of thousands of independent banks, and use their votes in unison, without running into any anti-trust laws. Which would in itself be quite a task. You'd literally have to have about enough money to supply the entire US economy for an entire year. And it would all have to be flowing underground. Then, to continue the conspiracy, your task would be made more difficult by the fact that banks only appoint 6 of the 9 governers. So, they'd have to control 5 banks out of every 6 in the United States to get a definite controlling share of all the federal reserve banks in the United States. THis would make up for the trillions of wasted dollars and the possibility of being executed if found.
Then, of course, none of those federal reserve banks can appoint anyone on the actual federal reserve board, so they'd only have limited control after that, unless they could bankroll the entire US congress and presidency into their shadowy cause, which would give them control over interest rates that could be used (I assume) to make their stocks go up somewhere.
Systems like this are very easy to create.