I wrote a term paper on this once.
The idea came from a writing of "Cato" (Governor George Clinton, supposedly, that may be in dispute) before the Constitutional Convention in which he suggested a triumvirate or something. [sorry, can't recall his argument off the top of my head.]
...and talked about the ceremonial necessity of the President at the OWC....
I think it is a good idea for the polis but people aren't psychologically ready. Suggesting such a change frightens people and most will dismiss it as crazy, and it is in the sense that you don't mess something when it still seems to be working. And our language and customs still center on a lawgiver represented by the President, so it helps keep cohesiveness.
Of course, I don't think it does- or it soon won't- but that is speculating three steps ahead. Ha. A quick run down is:
-Keep a ceremonial Presidency elected by the Senate ratified by the States electoral voters. He or she would have to have no party affiliation and must be out of politics for 5 to 10 years (something like that) before taking office. The term would be 8 years.
-The President would elect Two Vice-Presidents: One would be an emergency replacement during his term. The other would be in the Legislative branch- read Jefferson and Senator Clay for a good example of what the office would entail- and represent the executive branch, but like now, no vote unless a tie.
-Eliminate several departments and get it down to five secretaries. Each department would be directly elected by the people for 4 year terms. The President could ostensibly be as a chief of staff.
-Repeal the 17th amendment and give the power to appoint Senators back to the States. Ramp up the number of representatives to better represent groups of people.
The idea would be to try to choke the money system while giving the people more choice, it would be much harder to lobby 800 representatives and then have to lobby all 50 states then five secretaries...etc....