What you need isn't an amendment to patch the symptoms(although that should really be done anyway), you really ought to change your outdated federal election system, it's 200 years out of date, it was necessary for running a large country 200 years ago because communication was hard back then. Especially with a small federal state without far reaching powers but nowadays your federal state is just as large as any other government with the federal government running most things it chooses to run. And this is a good thing in my opinion, a small state doesn't work, that just means you're giving corporations a free run to do whatever they want, you need a large with lots of regulations and investigative powers to keep the corporations in check, you need a large government which can say you broke the law so now we're seizing your assets wether you want to or not.
There's really not that much difference between the US and a smaller country. Therefore the US needs to make it easier to get a seat in congress/senate, instead of the extremely crappy "first one across the line" you inherited from the british.
If it was easier to elect someone into power(and thus out of power) and easier for parties to get representation in the senate/congress(such as a proportional election) where you don't need to get 50% of the votes in a district to get that districts seat(which is bloody hard, nearly impossible except for 1-2, maaaybe 3 parties), instead if you get 10% of the votes(which is a whole lot easier because your sympathizers don't need to all live in one place) you get 10% of the seats.
Maybe then the voter turnout could go up because people might actually feel that their vote is worth something. And if it's easier to get rid of corrupt politicians who take bribes("campaign contributions") then maybe you could return power to the masses rather than leave it in the hands of the wealthy.
Because as long as you keep your current election system you're not gonna get the other ones fixed because the politicians will NEVER prevent the corporations from bribing them, not after they've gotten a taste of it. Power begets power, for the sake of power.