Here are some suggestions I've seen/made that to me offer a pathway out of the current stagnation:
An amendment enforcing one person, one vote. If the right to bear arms can be protected (regardless of the discussion over wether it ever pertained to an individual right), the right to vote should be,as well. The government cannot take any measure that infringes on the right to vote except in cases where it can prove there is actual fraud or some other anti-democratic effect.
Move past the current first-past-the-post election system. I'm still not sure if multi member districts or ranked choice voting or a combo works best. It's appropriate to try all in different states and then put the question to a national referendum. Speaking of...
Institute a national referendum system. The way I think this should work is national referendum items are on the same ballot as the Presidential candidates. 33% of the population, regardless of geography, has to vote first to even allow the question. If an issue clears that threshold, the next cycle, it'll be up for a national vote, where it'll need to hit 50% or more to pass, and such a passed law has the same force as a constitutional amendment. The numbers can be tweaked, but you need a way for citizens to cut through Congressional gridlock.
Term limits on the Supreme Court. Another thing that needs a Constitutional amendment, but it's worth it, I feel. 18 year terms make perfect sense, here. I've also liked the idea of having a 15 member court, only 5 of whom will be assigned to any given case, at random. This means you can't predict the partisan divide of the court for a case, which reduces the need to obsess over each Justice who gets sworn in, and might help reverse the recent trend of picking idealistically extreme candidates.
This isn't an amendment, but both House and Senate rules need to change to allow any bill on the floor that has, say, 40% support, regardless of party affiliation. As it is, centrists just cannot band together to pass common sense laws if the Majority leader/Speaker, in the hopes of playing to the base, refuses to even allow the bill to the floor.
Election administration needs to move to a non-partisan commission, both at the state and federal levels. It's insane that elections are administered by the very people participating in them as candidates. It's one of the most regressive features of American democracy, and plays no small part in the current state of affairs. It allows parties to not be responsive to broader public opinion by allowing them to dice up the public to suit their political leanings. Instead of voters picking candidates, you have candidates picking voters.