Myth
The states can only apply for a convention. They really have no other control over the process. Congress has all the control.
Fact
The fact is - it is the states that have all the control in the convention process.
Founders intent
And we know that's what the founder intended because they said as much during the ratification debates. From the debates in PA...
"That the proposed Federal Constitution cannot be very dangerous while the legislature[s] of the different states possess the power of calling a convention, appointing the delegates and instructing them in the articles they wish altered or abolished."