The commission of the original Constitutional Convention was to propose amendments to the Articles of Confederation. Although they were not authorized to do so, the Framers decided not to amend it, but to replace it. Could a modern Constitutional Convention do the same thing? Yes.
Technically, the Articles of Confederation could not be amended without the consent of each and every state in the United States. If the Constitution was an amending document, it was illegal. This was well-known at the time. The Constitution itself was produced in strictest secrecy during the Philadelphia convention. When the Congress that had commissioned the work, the Congress of the Articles of Confederation, found out what the Framers had done, they considered censuring the delegates for having both failed to do their job and for violating the law.
Instead, like many legislators today, they decided to punt. Not only was no one prosecuted, the Congress kicked the whole thing back to state conventions.
Now, the Articles of Confederation called for unanimous consent. But that rule was thrown out and replaced by "nine of thirteen." Today, those in favor of a convention argue that 37 states must pass any changes. Well, maybe. But maybe not. If the last Constitutional Convention could throw out the requirement for unanimity, what on earth prevents the next one from throwing out the requirement for 37 out of 50 states? Why not just a bare majority? Or perhaps discard the need for states at all, and go to passage by a certain number of large (as some arbitrary person defines "large") cities? After all, why should the state of Montana (entire population: 1.02 million) have more say then the city of Los Angeles (population 18.55 million)?
And remember what Congress did? They kicked it to state conventions. In order to keep state legislatures from adding on their own amendments, the state legislators and their legislatures were entirely cut out of the process. Instead, special state conventions voted on whether or not to approve it.
The first state to ratify was Delaware, on December 7, 1787. On June 21, 1788, New Hampshire became the ninth state to ratify and the Confederation Congress set the new Constitution's operational date as March 4, 1789, but that left four states out in the cold. Virginia and New York ratified it by July of 1788, but the remaining two did not ratify it before it became operational.
The Constitution was essentially imposed on North Carolina, which didn't ratify until November 21, 1789, and on Rhode Island. In fact, the last state, Rhode Island, didn't ratify it until May 29, 1790. By the time Rhode Island finally made it unanimous, the first Congress had already been in session for over a year (convened March 4, 1789, didn't release until March 4, 1791) and George Washington had already been President for over a year. In other words, at least two of the four states named above were forced to go along with a document, the Constitution, that even their own state conventions didn't approve. If this is a model for the interaction between states' rights and federal power, you can see who wins very early on.
If we look at it from the point of view of the Articles of Confederation, by September 13, 1788, eleven states had illegally seceded from the Articles. If North Carolina and Rhode Island would have had the military capacity, they could legally have declared this a rebellion and forced the eleven ratifying states back into the Articles of Confederation in exactly the same way Lincoln forced the Southern States back into the Constitution eighty years later.
Now, with this in mind, consider what the map of state legislatures looks like today:
Does anyone think today's process would run any smoother? Can we afford a couple of years of political anarchy while we try to get everything squared away with a new Constitution? Because anyone who thinks we won't get an entirely new Constitution, along with a whole new set of rights (which may or may not reflect any of our current rights), really isn't paying attention.
What makes you think a new Article V convention would treat the Constitution with any more respect than the the original convention treated the old Articles of Confederation?
We already have a political elite who argue that the Constitution is not a good structure for America nor a good model for new democracies in the 21st century. This same political elite controls the media and a lot of the political processes, they control the colleges and universities from which "expert" advisors will be drawn.
These are the people that got Obama elected.
What makes you think we could stop them at a convention?