"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..."
Looks like the legislatures may vote on whether or not to ratify a proposed amendment without regard to whether or not any particular one of them has or doesn't have the power to do whatever the amendment authorizes.
More to the point of this thread:
Can a legislature vote to give the federal government the power to do something that they themselves do have the power to do?
Can the people vote to give the federal government the power to do something that they themselves do have the power to do?
Yes.. -- As long as the powers do not violate the US Constitution.
-- And, we cannot Amend the Constitution in ways that are repugnant to its basic principles. [This is why the income tax is seen as unconstitutional, as was prohibition.]