My third novel covers the nightmare resulting from a runaway con-con.Only in a novel is such a concern. There is NO SUCH THING as a "CON-CON" in our system. Period.
There IS an "Amending Convention" that may PROPOSE to the States Amendments, but that is ALL that it can do.
Try reading the Constitution once in a while.
The Congress, whenever two thirds of both Houses shall deem it necessary, shall propose Amendments to this Constitution, or, on the Application of the Legislatures of two thirds of the several States, shall call a Convention for proposing Amendments, which, in either Case, shall be valid to all Intents and Purposes, as part of this Constitution, when ratified by the Legislatures of three fourths of the several States, or by Conventions in three fourths thereof, as the one or the other Mode of Ratification may be proposed by the Congress;