The US Senate is designed to check and balance the House of Representatives. But that often puts the Congress as a whole in deadlock, meaning it can no longer balance the other two branches.
When they could get anything done they delegated a lot of power to the Executive. Which worked ok, but eventually a "unitary executive" appropriated even more power, and the Legislature is powerless to prevent it.
Unpopular opinion: deadlock is fine. Most legislation is bad. What really matters is the budget. And the rule that failing to pass a budget can automatically force an election avoids the absurd US "shutdown" that isn't a shutdown.
This is now my second favorite idea, after a nationwide ban of first past the post voting schemes.
My third (previously second) is outlawing political parties. The problem with that one is it would be really difficult to implement in a way that doesn't run afoul of freedom of association and freedom of speech. Probably worth figuring out though.
Voting system reform would probably mitigate the worst aspects of political parties.
Egypt after ousting Mubarak held an election where a third of seats were reserved for independents. Most winning candidates were just Muslim Brotherhood affiliated. I suspect the military interim government did that deliberately to justify their later coup.
On the other hand, voting needs to mean something. If voting doesn't mean anything, because the whole system is held in a vice grip by a sclerotic institution playing power games with itself, then the broader system eventually collapses.
My personal opinion is that Mitch McConnell's intransigence and unwillingness to do anything lest Obama get credit for it led directly to an increased desire for a "strongman"