Now here's my plan ...

Like many of my friends I am fed up with the two-party system in the US.  Sadly, the system is the inevitable result of how our voting system works.  A while back I realized that the US could be changed into a parliamentary government without any constitutional amendments.

Let me be clear, I don't think this is likely at all to happen.  In fact I think there are some significant problems with this plan.  That said, I see it more as an example of how flexible (or even hackable) our government was designed to be.

Congress

First we need to switch the House of Representatives to be more diverse.  This would require changing federal and state laws - for example the 1967 Uniform Congressional District Act (which mandates single-member districts) would probably need to be repealed. Instead voters would select a party (or individual acting as a party) to represent them and the state's seats in the House would be proportionally divided up according to the results.

The Senate?  Leave them as they are, I suppose.  If anyone has good ideas for the Senate I'm happy to listen.

Presidency

Here's the fun part.  The constitution requires a presidential election every four years, but it doesn't require us to actually keep the result.

The 25th amendment allows for removing the president from office if they're deemed unable to discharge the powers and duties of his office. The amendment says this can be done by the Vice President and principle officers of the administration, however it goes on to add "... or of such other body as Congress may by law provide."  

So Congress could pass a law stating that Congress can declare the president unable to do the job.  Effectively this would be a vote of no confidence.

So every four years there's a symbolic presidential election and the winner becomes President.  Then Congress would vote no confidence and the President is removed from office (the President could object in writing but then Congress would hold another vote and it would still happen).  That means the VP would assume the office of President ... and Congress would remove them too.

The presidency would then pass to the Speaker of the House ... who was just elected to that position by the house so it would probably stick.  A new Speaker is chosen, and a new VP would be appointed and confirmed by ... the House.

What this results in is a House of Representatives that is more representative, and a presidency that can be replaced at any time.

We could still keep the presidential elections and even the Electoral College - though really there'd be no point to them.