Start by electing principled people. If they turn, vote them out or recall where legal to do so. Simple. All it lacks is people with the integrity to follow through.
That was how the founders designed the system afterall.
While no republic can long survive a corrupt citizenry, there is more to the Framers' design. They divided power, and not just horizontally between the three branches. The first and most important division was between the states and the government they created.
Our silly tack-on, the 17th Amendment is like adding a rumble seat to a Miata sports car. It can be done, but both screw up terrific designs.