No you can't because of the brief nature of the Constitution and its silence on many matters
You know, it would help immensely if you took some college level courses on government and political science.
Since you'll probably never muster up the courage to do that, I'll explain it to you and the perhaps you'll understand the meaning of the word "elegant."
Let's take the Presidency.
The Framers could have enumerated every right that the President as head-of-State has.
That section of the Constitution alone would be about 19,473 pages.
Get it?
A more elegant way is simply to assume that a President has all the rights a head-of-State has had since time immemorial and then enumerate only those powers that were barred or limited.
Since time immemorial, heads-of-State have had the power to declare war. The Framers decided to take away that right and give it to the People and the States
vis-a-vis Congress.
Since time immemorial, heads-of-State have had the right to choose their Cabinets. The Framers limited that power by having the States
vis-a-vis the Senate approve the appointments.
Heads-of-State also had the exclusive right to enter into treaties, and the President still does, but that power is checked by the States requiring Senate approval.
Heads-of-State also had the power to levy taxes, but the Framers gave that power to the People via the House.
See how that works? And it works for everything.
Take
Ashcroft.
Someone sued saying the Secretary of Defense does not have the power to close military bases. The Supreme Court said they were wrong. A Cabinet member does have that power and even though it isn't spelled out in writing in the Constitution, it is a traditional power of that specific Cabinet office and that power was extant in the Articles of Confederation, the Continental Congress and the Stamp Tax Congress.
Congress has all the traditional powers the Roman Senate and the Greek democracies had. Most of the powers enumerated are powers a head-of-State had but were given expressly to Congress by the Framers or split between the two houses in keeping with a bicameral legislature.
If the Framers were to enumerate every stinking power, your Constitution would be a 144 volume set of more than 100,000 pages.
For instance, did the framers ever envision secession by one state or more ?
The People have that right under the Continental Congress and the Stamp Tax Congress.
Under a parliamentary system, you can have various forms of voting, you can elect your head of state or appoint them through birthright
I cannot think of a single advantage that a presidential system has over a parliamentary system.
That's because you allowed yourself to become mired with only 2 political parties.
Under your Constitution, it is the Speaker of the House that was supposed to have the real power. Weak politicians handed off most of their power to the President over the years, in part because a lot of them early on were monarchists and would have preferred a king to a president.
Your system is perfectly capable of handling multiple parties. If you had 12 political parties, the Speaker would be chosen by a coalition of parties, just like in a parliamentary system.
Your system is screwed up because you allow the sovereignty of States to be egregiously violated and monied interests to buy votes.
